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Ill  II II  A  It 

OF   THE 

of 


Name  of  Book  and  Volume, 


AN 

ELEMENTARY 

AND 

PRACTICAL    TREATISE 

ON 

BRIDGE  BUILDING, 

AK 

•4 

ENLARGED  AND  IMPROVED  EDITION 

OF  THE  AUTHOR'S  ORIGINAL  WORK, 


S.    WHIPPLE,    C.E. 

ALBANY,    N.   Y., 
IHYENTOR  OF  THE  WHIPPLE  BRIDGES,  M*. 


SECOND   EDITION,  REVISED   AND   ENLARGED. 


NEW  YORK: 

1).   VAN    NOSTRAND,    PUBLISHER, 

23  Murray  St.,  and  27  Warren  St. 

18T3. 


Entered  according  to  Act  of  Congress,  in  the  year  1873,  bj 

S.    WHIPPLE, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


INTRODUCTION. 


It  is  about  thirty  years  since  the  An  thor's  attention 
was  especially  directed  to  the  subject  of  BRIDGE 
CONSTRUCTOR;  and,  Lis  Original  Essays  published 
in  1847,  are  believed  to  have  aided  considerably 
toward  establishing  the  foundation  upon  which  a 
knowledge  of  the  principles  involved,  and  the  con 
ditions  required  in  the  proper  construction  of  TRUSS 
BRIDGES,  has  been  built  up,  and  carried  to  a  high 
state  of  advancement. 

However  that  may  be,  the  flattering  terms  in 
which  his  former  labors  in  the  premises  have  often 
been  referred  to,  as  well  as  the  frequent  applications 
for  copies  of  his  former  publication,  since  the 
supply  became  exhausted,  have  prompted  the 
issue  of  the  present  volume. 

This  work  inculcates  the  same  development  of 
GENERAL  PRINCIPLES,  and  treats  of  essentially  the 
same  General  Plans,  Combinations,  and  proportions 
for  bridge  work,  as  were  discussed  and  recom 
mended  in  its  humble  predecessor;  with  such 


iv  INTRODUCTION. 

additions  and  improvements  as  subsequent  experi 
ence  and  observation  have  enabled  the  Author  to 
introduce. 

The  design  has  been  to  develop  from  Funda 
mental  Principles,  a  system  easy  of  comprehension, 
and  such  as  to  enable  the  attentive  reader  and 
student  to  judge  understandingly  for  himself,  as 
to  the  relative  merits  of  different  plans  and  combi 
nations,  and  to  adopt  for  use,  such  as  may  be  most 
suitable  for  the  cases  he  may  have  to  deal  with. 

It  is  hoped  the  work  may  prove  an  appropriate 
Text  Book  upon  the  subject  treated  of,  for  the 
Engineering  Student,  and  a  useful  manual  for  the 
Practicing  Engineer,  and  Bridge  Builder.  But  as 
to  this,  the  decision  must  be  left  to  those  into  whose 
hands  it  may  fall;  and  to  that  arbitrement,  with 
out  further  remark  or  explanation,  it  is  respect 
fully  submitted. 


CONTENTS. 


Page. 

Preliminary  remarks,  &c.       --..--  1 

Two  Panel  Trusses             .......  9 

Three  Panel  Trusses      -                  16 

Five  Panel  Trusses             -                  ...  20 

Seven  Panel  Trusses.     The  Arch  Truss           -         -  31 

Trapezoid  Trusses  with  Verticals         ....  4G 

Trapezoid  Trusses  without  Verticals        ....  54 

Decussation  of  forces,  &c.            .....  64 

The  Warren  Uirder 69 

The  Finck  Truss       -                          ....  73 

Characteristics  of  the  Arch 74 

Weight  of  Structure                     -  77 

Double  Cancelated  Trusses  with  Verticals  80 

Double  Cancelated  Trusses  without  Verticals  fcG 

Decussation  in  Trusses  with  Verticals               -         -  92 

Deck  Bridges             -                  97 

Katio  of  length  to  depth  of  Truss  -                  ...  100 

Inclination  of  Diagonals               -         -         -         -         -  104 

Width  of  Panel     ...                  ....  109 

Arch  Bridges                                          -  112 

Construction  of  equilibrated  Arches         -         -         -         -  114 

Webbed  Arches         -                  -                            -  117 

Ordinates  of  equilibrated  curves  determined  by  calculation  119 

Action  of  the  web  in  webbed  Arches                     -         -  125 

Effects  of  heat  upon  Arches  without  Chords   -         -         -  126 

Bridge  Materials,  Wood  and  Iron  compared         -         -  132 

IRON  BRIDGES.  Strength  of  Iron  -  -  142 

Experiments  on  Cast  Iron,  &c.  ....  146 

Safe  practical  strain  of  Iron  .....  151 
Note  giving  examples  of  stress  of  Wrought  Iron  in  several 

structures  in  use  -  -  153  to  155 
Table  of  Negative  Strength  of  Iron  in  pieces  of  various 

lengths  and  sections 159 


vi  CONTESTS. 

Pa<jc. 

TRANSVERSE  strength  of  Iron                              .     161  to  171 

ARCH  TRUSS  BRIDGES 17_> 

Iron  Beams  for  Bridges                182 

Modes  of  Insertion  of  Iron  Beams           ....  184 

The  Link  Chord        -                                       -         -         -  188 

The  Eve-bar  Chord ]^2 

Size  of  connecting  Pins      -                   -         -         •         -  193 

Riveted  Plate  Chord      -                   19(j 

Trapezoidal  Truss  Bridges, —  details             ...  200 

Double  Cancelated  Bridges, —  details      ....  205 

Wrought  Iron  thrust  members            ....  214 

Double  Chord,  a  suggestion              .....  224 

Rivet-work  Bridges 227 

Sway-bracing                            ......  236 

Comparison  of  Bridge  Plans 241 

Bullman  Truss       -                    241 

Finck  Truss      -                            -  244 

Post  Truss                      246 

W hippie  Trapezoid             -  251 

The  Isometric  (without  verticals)  .....  253 

The  Arch  Truss                             256 

Synopsis  of  results  of  analyses 257 

(General  Remarks       -                   258 

COUNTER  BRACING, — value  of 263 

WOODEN  BRIDGES  — Strength  of  timber     -         -  274 

Table  of  Negative  resistance  of  timber    -         ...  276 

Transverse  strength  of  Wood 277 

Resistance  to  cleavage 278 

Connections  of  Tension  pieces     .....  279 

Connecting  pins  of  Wood  and  Iron         ....  281 

Splicing                                                   .  285 

Construction  of  Wooden  Trusses 288 

Two  panel  Wooden  Truss  Bridge        ....  288 

Three  panel  Wooden  Truss  Bridge         ....  294 

Four  and  Six  panel  Wooden  Truss  Bridge           -         -  296 

The  Howe  Bridge 302 

Wooden  Trapezoid  without  verticals             ...  30$ 

MODULUS  of  strength  of  Trusses             ....  314 


BRIDGE   BUILDING. 


PRELIMINARIES. 

I.  A  bridge  is  a  structure  for  sustaining  the  weight 
of  carriages,  animals,  &c.,  during  their  transit  over  a 
stream,  gulf  or  valley. 

Bridges  are  constructed  of  various  plans  and  dimen 
sions,  according  to  the  circumstances  and  objects  re 
quiring  their  erection  ;  and  it  is  the  purpose  of  this 
work,  after  a  few  remarks  upon  the  general  nature  and 
principles  of  bridges,  to  attempt  some  analyses  and 
comparisons  of  the  respective  qualities  and  merits  of 
various  general  plans,  with  a  view  of  deducing  practi 
cal  results,  as  to  a  judicious  and  economical  choice  and 
application  of  materials  in  the  construction  of  these 
useful  and  important  structures. 

II.  The  force  of  gravity,  on  which  the  weight  of 
bodies  depends,  acts  in  vertical  lines,  and  consequently, 
a  heavy  body  can  only  be  prevented  from  falling  to  the 
earth,  by  a  force  equal  and  opposite  to  that  with  which 
gravity  impels   the  body   downward.     This  resisting 
force  must  not  only  act  vertically  upward,  but  the  line 
of  its  action  must  pass  through  the  centre  of  gravity  of 
the  body  it  sustains.     All  the  forces  in  the  world,  act 
ing  parallel  with,  or  perpendicular  to,  the  vertical  pass 
ing  through  its  centre  of  gravity,  could  not  prevent  a 

1 


2  BRIDGE  BUILDING. 

musket  ball  (concentrated  to  the  point  of  its  centre  of 
gravity)  from  falling  to  the  centre  of  the  earth,  unless 
it  were  a  horizontal  force  capable  of  giving  the  ball  a 
projection,  such  that  the  centrifugal  tendency  should 
equal  or  exceed  gravity  —  a  kind  of  force  which  could 
never  be  made  available  toward  preventing  people  from 
falling  into  the  water  in  crossing  rivers  ;  consequently, 
having  no  application  in  bridge  building. 

In  fact,  nothing  but  a  continuous  series  of  unyielding 
material  particles,' extending  from  an  elevated  body 
downward  to  the  earth,  can  hold  or  sustain  that  body 
above  the  earth,  by  vertical  and  horizontal  action 
alone,  either  separately,  or  in  combination. 

* 

III.  Suppose  a  body,  no  matter  how  great  or  small, 
placed  above  the  earth,  with  a  deep  void,  or  an  inac 
cessible  space  benea'th  it.  Attach  as  many  cords  to  it 
as  you  please,  strain  them  much  or  little  —  only  hori 
zontally  —  the  body  will  fall,  nevertheless.  Thrust  any 
number  of  rods,  with  whatever  force  you  may,  hori 
zontally  against  it;  still  the  body  will  fall.  This  is 
obvious  from  the  fact  that  horizontal  forces,  acting  at 
right  angles  with  the  direction  of  the  force  of  gravity, 
have  no  more  tendency  to  prevent,  than  to  promote 
the  fall  of  the  body. 

Moreover,  the  space  beneath  being  inaccessible, 
there  is  no  foundation,  or  foot  hold,  upon  which  to 
rest  a  post  or  stud  that  may  directly  resist  the  action 
of  gravity,  while  the  lines  of  all  other  vertical  forces  or 
resistances,  pass  by  the  body  without  touching  it. 

In  the  case  here  supposed,  the  body  can  only  be  pre 
vented  from  falling  by  oblique  forces;  that  is,  by  forces 
whose  lines  of  action  are  neither  exactly  horizontal, 
nor  exactly  perpendicular.  Attach  two  cords  to  the 


PRELIMINARIES.  3 

body,  draw  upon  them  obliquely  upward  and  outward, 
in  opposite  directions,  or  from  opposite  sides  of  the 
void,  with  a  certain  stress,  and  the  body  will  be  sus 
tained  in  its  position.  Apply  two  rods  to  it  obliquely 
upward,  of  a  proper  degree  of  stiffness,  in  the  same 
vertical  plane,  and  on  opposite  sides  of  the  perpendicu 
lar,  a  certain  thrust  exerted  upon  those  rods,  will  pre 
vent  the  descent  of  the  body. 

IV.  Sere,  then,  we  have  the  elementary  idea  —  the 
grand  fundamental  principle  in  bridge  building.  What 
ever  be  the  form  of  structure  adopted,  the  elementary 
object  to  be  accomplished  is,  to  sustain  a  given  weight 
in  a  given  position,  by  a  system  of  oblique  forces,  whose 
resultant  shall  pass  through  the  centre  of  gravity  of  the 
body  in  a  vertically  upward  direction,  in  circumstances 
where  the  weight  can  not  be  conveniently  met  by  a  sim 
ple  force,  in  the  same  line  with,  and  opposite  to,  that 
of  gravity. 

For  a  more  clear  illustration  of  this  elementary  idea, 
let  us  suppose  a  a',  Fig.  1,  to  represent  the  banks  of  a 
river,  or  the  abutments  of  a  bridge ;  and  ggr,  the  line 
of  transit  for  carriages,  &c. ;  and,  let  us  further  suppose 
a  load  of  a  certain  weight,  w,  to  have  arrived  at  a  point 
centrally  between  a  ar.  The  simplest  method  of  sus 
taining  the  weight  is,  perhaps,  either  to  erect  two  ob 
lique  braces  aw.  .  a'w,  or  suspend  two  oblique  chains 
or  ties  pw,  p'w,  from  fixed  supporting  points  a  a',  orppf. 

It  is  not  necessary  that  the  weight  be  at  the  angular 
point  w,  of  the  braces  or  chains,  but  it  may  be  sustained 
by  simple  suspension  at  wf  below,  or  simple,  support  at 
w"  above,  and  such  obliquity  may  be  given  to  the  braces 
or  chains  as  maybe  most  economical ;  a  consideration 
which  will  be  taken  into  account  hereafter. 


4  BRIDGE  BUILDING. 

V.  Thus  we  see  how  a  weight  may  be  sustained  cen 
trally  between  the  banks  of  a  river,  or  the  extremities 
of  a  bridge.  But  the  structure  must  not  only  provide 
for  the  support  of  weight  at  this  point,  but  also  at  every 
other  point  between  a  a',  orgy' ;  and  it  is  obvious  that 
the  same  plan  and  arrangement  will  apply  as  well  at 
any  other  point  as  at  the  centre,  with  only  the  variation 
of  making  the  braces  or  chains  of  unequal  length. 


This,  however,  would  require  as  many  pairs  of  braces 
or  chains  as  there  were  points  between  g  gf ,  a  thing, 
of  course,  impracticable,  since  the  oblique  members 
would  interfere  with  one  another,  and  be  confounded 
into  a  solid  mass.  We  therefore  resort  to  the  transverse 
strength  and  stiffness  of  beams, — phenomena  with 
which  all  have  more  or  less  acquaintance,  and  without 
digressing  in  this  place  to  investigate  their  principles 
and  causes,  it  will  be  assumed  as  a  fact  sustained  by  all 
experience,  that,  for  sustaining  weight  between  two 
supporting  points  upon  nearly  the  same  level,  a  simple 
beam  affords  the  most  convenient  and  economical 
means,  until  those  points  exceed  a  certain  distance 
asunder,  which  distance  will  vary  with  circumstances ; 


PRELIMINARIES.  5 

but  in  bridge  building,  will  seldom  be  less  than  10  to 
14  feet,  where  timber  beams  are  employed.  Hence, 
for  bridges  of  a  length  of  12  to  14  feet,  usually,  nothing 
better  can  be  employed  than  a  structure  supported  by 
longitudinal  beams,  with  their  ends  resting  upon  abut 
ments  or  supports  upon  the  sides  of  the  stream. 

Of  course,  no  reference  is  here  had  to  stone  or  brick 
arches.  For,  though  these  are  advantageously  used 
for  short  spans,  and  in  deep  valleys,  where  the  ex 
pense  of  constructing  high  abutments  for  supporting  a 
lighter  superstructure,  would  exceed  or  approximate  to 
that  of  constructing  the  arch,  it  is  the  purpose  of  this 
work  to  speak  only  of  those  lighter  structures,  com 
posed  mostly  of  wood  and  iron,  and  supported  by  abut 
ments  and  piers  of  stone,  or  by  piles,  or  frames  of  wood. 

Having  then  adopted  the  use  of  beams  for  supporting 
weight  upon  short  spaces,  it  is  only  necessary  upon 
longer  stretches,  to  provide  support  for  a  point  once 
in  10  or  14  feet,  by  braces,  &c.,  from  the  extremities; 
and  for  intermediate  points,  to  depend  on  beams  or 
joists  extending  from  one  to  another  of  the  principal 
points  provided  for  as  above.* 

VI.  For  a  span  of  20  or  30  feet,  it  would  seem  that 
no  better  plan  could  be  devised,  than  to  support  a 
transverse  beam  midway  between  abutments,  by  two 
pairs  of  braces  or  suspension  chains,  proceeding  from 
points  at  or  over  the  abutments,  one  pair  upon  each 
side  of  the  road- way ;  this  transverse  beam  affording 
support  for  longitudinal  beams  or  joists  extending 


*  It  is  susceptible  of  easy  demonstration  that  the  power  of  beams  to 
sustain  weight  by  lateral  stiffness,  forms  no  exception  to  the  principle 
that  oblique  forces  alone  can  sustain  heavy  bodies  over  inaccessible 
epaces.  But  this  matter  is  deferred  for  the  present. 


6  BRIDGE  BUILDING. 

therefrom  to  the  abutments.  When  suspension  chains 
are  used,  it  may  properly  be  called  a  suspension  bridge. 
If  braces  be  employed,  it  is  usually  termed  a  truss-bridge. 


HORIZONTAL  ACTION  OF  OBLIQUE  MEMBERS. 

VII.  Before  advancing  further,  it  will  be  proper  to 
refer  to  an  important  principle  or  fact  which  has  not 
yet  been  taken  into  account,  though  a  fact  by  no  means 
of  secondary  interest. 

The  sustaining  of  weight  by  oblique  forces,  gives  rise 
to  horizontal  forces,  for  which  it  is  necessary  to  provide 
counteraction  and  support,  as  well  as  for  the  weight  of 
the  structure  and  its  load.     The  two  equal  and  equally 
inclined  braces,  ac  and  6c,  Fig. 
2,  in  supporting  the  weight  w 
at  c,  act   in   the   directions  of 
their   respective   lengths,    each 
with   a  certain   force,  which  is 
-.  --  equivalent    to     the    combined 

^  action  of  a  vertical  and  a  hori 
zontal  force,  [Elementary  Mechanics — Statics^]  which 
may  be  called  the  vertical  and  horizontal  constituents 
of  the  oblique  force.  These  two  constituent  forces 
bear  certain  determinate  relations  to  one  another, 
and  to  the  oblique  force,  depending  upon  the  angle 
at  which  the  oblique  is  inclined. 

Now,  we  know  that  the  vertical  constituent  alone 
contributes  to  the  sustaining  of  the  weight,  and  conse 
quently,  must  be  just  equal  to  the  weight  sustained,  in 
this  case  equal  to  -J?.#.  We  know  moreover,  from  the 
principles  of  statics,  that  three  forces  in  equilibrio, 
must  have  their  lines  of  action  in  the  same  plane,  and 


PRELIMINARIES.  7 

meeting  at  one  point ;  and  must  be  respectively  pro 
portional  to  the  sides  of  a  triangle  formed  by  lines 
drawn  parallel  with  the  directions  of  the  three  forces; 
and  that  each  of  the  three  forces  is  equal  and  opposite 
to  the  resultant  of  the  combined  action  of  the  other 
two.  We  have,  then,  at  c,  the  weight  J  w,  the  oblique 
force  in  the  line  ac,  and  a  third  force,  equal  and  oppo 
site  to  the  horizontal  constituent  of  the  oblique  force 
in  the  line  ac.  Then,  letting  fall  the  vertical  dc9  and 
drawing  the  horizontal  ad,  the  sides  of  the  triangle  acd, 
are  respectively  parallel  with  the  three  forces  in  equili- 
brio  at  the  point  c.  Hence,  representing  the  vertical 
cd9  by  v,  the  horizontal  ad,  by  h9  and  the  oblique  by  o ; 
and  calling  the  horizontal  force  x,  and  the  oblique 
force,  y9  we  have  the  following  proportions  : 

(1).          Jw  :  x  :  :  v  :  A,  whence,  x  =  J  w— 
(2).          JMJ  :  y  :  :  v  :  o,  whence,  y  =  %w  °— 

But  \w  equals  the  weight  sustained  by  the  oblique 
ac.  Therefore,  from  the  two  equations  above  deduced, 
we  may  enunciate  the  following  important  rule  : 

The  horizontal  thrust  of  an  oblique  brace,  equals  the 
weight  sustained,  multiplied  by  the  horizontal  and 
divided  by  the  vertical  reach  of  the  brace ;  and  the 
direct  thrust  (in  the  direction  of  its  length),  equals  the 
weight  sustained  multiplied  by  the  length,  and  divided 
by  the  vertical  reach  of  the  brace. 

VIII.  Now,  it  is  obvious  that  the  brace  exerts  the 
same  action,  both  vertically  and  horizontally,  at  the 
lower,  as  at  the  upper  end,  though  in  the  opposite 
directions;  the  brace  being  simply  a  medium  for  trans 
mitting  the  action  of  weight  from  the  upper  to  the 


8  BRIDGE  BUILDING. 

lower  end  of  the  brace.  Hence,  the  weight  sustained 
by  the  brace  ac,  exerts  the  same  vertical  pressure  at 
the  point  a,  as  it  would  do  if  resting  at  that  point, 
while  the  brace  requires  a  horizontal  resistance  to  pre 
vent  its  sliding  to  the  left,  as  would  be  the  case  if  its 
foot  simply  rested  upon  a  smooth  level  surface.  This 
horizontal  resistance  may  be  provided  by  abutments 
of  such  form,  weight,  and  anchorage  in  the  earth,  as  to 
enable  them  to  resist  horizontally  as  well  as  vertically, 
or  by  a  horizontal  tie,  in  the  line  a6,  connecting  the 
feet  of  opposite  braces. 

These  two  methods  are  both  feasible  to  a  certain  ex 
tent,  and  in  certain  cases ;  and,  both  involve  expense. 
Under  particular  circumstances,  it  may  be  a  question 
whether  the  former  should  not  be  resorted  to,  wholly 
or  partially.  But  for  general  practice,  in  the  construc 
tion  of  bridges  for  heavy  burthens,  such  as  rail  road 
bridges,  and  especially  iron  truss  bridges,  where  expan 
sion  and  contraction  of  materials  produce  considerable 
changes,  it  is  undoubtedly  best  to  provide  means  for 
withstanding  the  horizontal  action  of  obliques,  within 
the  superstructure  itself;  and  this  principle  will  be  ad 
hered  to  in  the  discussions  following. 

The  preceding  remarks  and  illustrations  as  to  the  ac 
tion  of  braces,  or  thrust  obliques,  obviously  apply  in 
like  manner  to  obliques  acting  by  tension,  with  only 
the  distinction,  that  in  the  latter  case,  the  weight  is 
applied  at  the  lower,  and  its  action  transmitted  to  the 
tipper  end  of  the  oblique,  and  the  horizontal  action  (at 
the  remote  end),  is  inward,  and  toward  the  vertical 
through  the  weight,  instead  of  outward ;  and  conse 
quently,  must  be  counteracted  by  outward  thrust,  as 
by  a  rigid  body  between  the  points  p  p',  Fig.  1,  or  by 
heavy  towers,  and  anchorage  capable  of  withstanding 


Two  PANEL  TRUSSES.  9 

the  inward  tendency.  Hence,  in  applying  the  rule  be 
fore  given,  to  tension  obliques,  and  their  vertical  and 
horizontal  constituents,  the  word  pull  should  be  sub 
stituted  for  the  word  thrust,  wherever  the  latter  occurs 
in  said  rule. 


TWO  PANEL  TRUSSES. 

IX.  There   are  three  forms  of  truss   adaptable   to 
bridges  with  a  single  central   beam  or   cross   bearer 

(which  may  be  called  two 
panel  trusses),  the  general 
JT  characteristics  of  which, 

are  respectively  repre-- 
sented  by  Figures  3, 4  and 
5.  Fig.  3  represents  a 
pair  of  rafter  braces,  with 

feet  connected  by  a  horizontal  tie,  and  with  a  vertical 
tie  by  which  the  beam  is  suspended  at  or  near  the 
horizontal  tie,  or  the  chord,  as  usually  designated. 

For  convenience  of  comparison,  let  bd  =  v9=l,=  ver 
tical  reach  of  oblique  members  in  each  figure.  Also, 
let  each  chord  equal  4i?,  =  4,  and  the  half  chord  =  2  = 
h  =  horizontal  reach  of  obliques  in  Figs.  3  and  4.  Then 
ad,  Fig.  3,  equals  \/h*+v*  =»  \/5,  and  if  the  truss  be 
loaded  with  a  weight  w,  at  the  point  6,  bd  will  have  a 
tension  equal  to  w,  and  abc,  [see  rule  at  end  of  Sec. 
VII],  a  tension  equal  to  J?0,  (  =  weight  sustained  by  ad), 
multiplied  by  the  horizontal,  and  divided  by  the  ver 
tical  reach  of  ad ;  that  is,  equal  to  \  w^,  =  JM?  $,  =  w; 
while  ad  suffers  compression  from  end  to  end,  equal  to 
w.  But  ad=N/5  and  i?-»l.  Whence  ia  = 


12  BRIDGE  BUILDINQ. 

making  for  the  four  pieces,  2n  for  tension,  and  2M  for 
compression. 

The  tie  or  chord  In,  suffers  tension  equal  to  the  hori 
zontal  constituent  of  the  thrust  of  ql,  manifestly  equal 
to  the  weight  sustained  by  ql,  or  equal  to  J  w.  There 
fore,  the  length  being  equal  to  4,  the  material  required 
in  its  construction,  equals  2M.  The  remaining  mem 
ber  pq  (=  2)  sustains  compression  equal  to  the  com 
bined  horizontal  constituents  of  the  tension  of  mq,  and 
the  compression  of  ql,  each  of  said  constituents  equal 
to  %w,  making  compression  of  pq,  equal  to  w,  and  length 
being  2,  material  =  2M 

We  have  therefore,  for  this  plan  of  truss,  4M,  for 
thrust  material,  and  4M  for  tension  material,  which  is 
J  less  than  in  case  of  Figs.  3  and  4.  Consequently, 
this  plan  is  decidedly  more  economical  than  either  of 
the  others,  unless  the  compression  material  acts  with 
better  advantage  in  the  latter  than  the  former ;  that 
is,  unless  the  thrust  members  in  3  and  4,  have  a  greater 
power  of  resistance  to  the  square  inch  of  cross-section, 
than  those  in  Fig.  5. 

XIIT.  As  to  this,  both  theory  and  experiment  prove, 
as  will  be  shown  in  a  subsequent  part  of  this  work, 
that  the  long  thrust  members  in  bridge  trusses,  are 
liable  to  be  broken  by  deflection,  rather  than  by  a 
crushing  of  the  material ;  that  in  pieces  with  similar 
cross-sections,  with  the  same  ratio  of  length  to  diameter, 
the  power  of  resistance  to  the  square  inch  is  the  same. 
That,  since  the  cross-section  is  as  the  square  of  the  di 
ameter,  and  the  diameters  (in  similar  pieces),  as  the 
lengths,  the  absolute  powers  of  resistance  (being  as  the 
cross  sections),  arenas  the  squares  of  the  lengths. 

v 


Two  PANEL  TRUSSES.  13 

Hence,  if  the  corapressive  forces  acting  upon  two 
pieces  of  different  lengths,  be  to  one  another  as  the 
squares  of  the  lengths  of  pieces  respectively,  and  the 
diameters  be  as  the  lengths,  the  forces  are  as  the  cross- 
sections,  and  proportional  to  the  power  of  resistance  in 
each  case,  and  the  material  in  the  two  pieces,  acts  with 
equal  advantage,  as  far  as  regards  cross-section,  so  that 
the  products  of  stress  into  length  of  pieces,  are  the  true 
exponents  of  amount  of  material  required  in  the  two 
pieces  respectively.  It  follows,  that,  if  on  dividing  the 
forces  acting  upon  the  pieces  in  question  respectively, 
by  the  squares  of  the  lengths,  the  quotient  be  the  same 
in  both  cases,  the  two  pieces  have  the  same  power  of 
resistance  to  the  square  inch,  and  in  general,  the  greater 
the  value  of  such  quotient,  the  greater  the  power  per 
inch,  and  the  greater  the  economy,  though  not  neces 
sarily  in  the  same  precise  ratio. 

XIV.  Applying  this  rule  to  thrust  members  in  plan 
Fig.  3,  being  the  braces,  the  compressive  force  equals 
Jitf\/5,  and  square  of  length  =  5.  Hence  the  quotient 
^w  5/5  =  0.2236^. 

The  piece  Id  Fig.  4,  has  length  =  4  and  compression= 
w,  whence,  force  divided  by  square  of  length  gives  ^w 
=  0.0625w.  This  shows  the  material  to  be  capable  of 
sustaining  much  more  to  the  square  inch  in  the  former, 
than  in  the  latter  case,  though  it  does  not  give  the 
true  ratio.  On  the  other  hand,  ek  and  gi,  with  length 
«  1,  and  stress  =  J?0,  give  quotient  =  %w  =  0.5w. 
Hence,  with  similar  cross-sections,  these  parts  have 
greater  power  to  the  inch  than  either  of  the  former,  but 
not  enough  to  balance  the  inferiority  of  /«',  as  compared 
with  ad  and  do,  in  Fig.  3. 


12  BRIDGE  BUILDING. 

making  for  the  four  pieces,  2M  for  tension,  and  2M  for 
compression. 

The  tie  or  chord  In,  suffers  tension  equal  to  the  hori 
zontal  constituent  of  the  thrust  of  ql,  manifestly  equal 
to  the  weight  sustained  by  ql,  or  equal  to  J  w.  There 
fore,  the  length  being  equal  to  4,  the  material  required 
in  its  construction,  equals  2M.  The  remaining  mem 
ber  pq  (=  2)  sustains  compression  equal  to  the  com 
bined  horizontal  constituents  of  the  tension  of  mq,  and 
the  compression  of  ql,  each  of  said  constituents  equal 
to  %w,  making  compression  of  pq,  equal  to  w,  and  length 
being  2,  material  =  2M 

We  have  therefore,  for  this  plan  of  truss,  4n,  for 
thrust  material,  and  4M  for  tension  material,  which  is 
J  less  than  in  case  of  Figs.  3  and  4.  Consequently, 
this  plan  is  decidedly  more  economical  than  either  of 
the  others,  unless  the  compression  material  acts  with 
better  advantage  in  the  latter  than  the  former ;  that 
is,  unless  the  thrust  members  in  3  and  4,  have  a  greater 
power  of  resistance  to  the  square  inch  of  cross-section, 
than  those  in  Fig.  5. 

XIIT.  As  to  this,  both  theory  and  experiment  prove, 
as  will  be  shown  in  a  subsequent  part  of  this  work, 
that  the  long  thrust  members  in  bridge  trusses,  are 
liable  to  be  broken  by  deflection,  rather  than  by  a 
crushing  of  the  material ;  that  in  pieces  with  similar 
cross-sections,  with  the  same  ratio  of  length  to  diameter, 
the  power  of  resistance  to  the  square  inch  is  the  same. 
That,  since  the  cross-section  is  as  the  square  of  the  di 
ameter,  and  the  diameters  (in  similar  pieces),  as  the 
lengths,  the  absolute  powers  of  resistance  (being  as  the 
cross  sections),  are.as  the  squares  of  the  lengths. 

s         WW-dU- 


Two  PANEL  TRUSSES.  13 

Hence,  if  the  compressive  forces  acting  upon  two 
pieces  of  different  lengths,  be  to  one  another  as  the 
squares  of  the  lengths  of  pieces  respectively,  and  the 
diameters  be  as  the  lengths,  the  forces  are  as  the  cross- 
sections,  and  proportional  to  the  power  of  resistance  in 
each  case,  and  the  material  in  the  two  pieces,  acts  with 
equal  advantage,  as  far  as  regards  cross-section,  so  that 
the  products  of  stress  into  length  of  pieces,  are  the  true 
exponents  of  amount  of  material  required  in  the  two 
pieces  respectively.  It  follows,  that,  if  on  dividing  the 
forces  acting  upon  the  pieces  in  question  respectively, 
by  the  squares  of  the  lengths,  the  quotient  be  the  same 
in  both  cases,  the  two  pieces  have  the  same  power  of 
resistance  to  the  square  inch,  and  in  general,  the  greater 
the  value  of  such  quotient,  the  greater  the  power  per 
inch,  and  the  greater  the  economy,  though  not  neces 
sarily  in  the  same  precise  ratio. 

XIV.  Applying  this  rule  to  thrust  members  in  plan 
Fig.  3,  being  the  braces,  the  compressive  force  equals 
Jitf\/5,  and  square  of  length  =  5.  Hence  the  quotient 
j\w  5/5  =  0.2236^. 

The  piece  Id  Fig.  4,  has  length  =4  and  compression = 
w,  whence,  force  divided  by  square  of  length  gives  ^w 
=  0.0625w.  This  shows  the  material  to  be  capable  of 
sustaining  much  more  to  the  square  inch  in  the  former, 
than  in  the  latter  case,  though  it  does  not  give  the 
true  ratio.  On  the  other  hand,  ek  and  gi,  with  length 
*=  1,  and  stress  =  J?#,  give  quotient  =  \w  =  0.5w. 
Hence,  with  similar  cross-sections,  these  parts  have 
greater  power  to  the  inch  than  either  of  the  former,  but 
not  enough  to  balance  the  inferiority  of  /«,  as  compared 
with  ad  and  dc,  in  Fig.  3. 


14  BRIDGE  BUILDING. 

"With  regard  to  truss  Fig.  5,  ql  and  pn,  suffer  each 
compression  equal  to  Jz0%/2,  with  square  of  length  =  2, 
giving  quotient  =  Ji#\/2,  =  0.371w,  while  pq,  has  com 
pression  =  10,  and  square  of  length  =  4,  arid  quotient 
=  J|0  =  0.25z0.  Hence  it  appears  that  this  plan  not 
only  possesses  a  decided  advantage  in  the  less  amount 
of  action*  upon  materials,  but  also,  a  considerable  ad 
vantage  as  to  ability  of  compression,  or  thrust  members, 
to  withstand  the  forces  to  which  they  are  exposed. 

XV.  Still  another  modification  for  a  truss  to  support 
a  single  beam,  is  formed  by  reversing  Fig.  3,  thus  con 
verting  tension  members  into  thrust  members,  and  vice 
Versa;  the  oblique  members  falling  below,  instead  of 
rising  above  the  grade,  or  road-way  of  the  bridge.  In 
this  case,  the  long  horizontal  thrust  member  «c,  is  di 
vided  and  supported  in  the  centre,  and  its  economy  of 
action  becomes  the  same  as  that  of  pq,  in  Fig.  5 ;  and 
the  truss  gives  the  same  exponents  for  both  thrust  and 
tension  material  as  when  in  the  position  of  Fig.  3. 
This  arrangement  affords  no  side  protection,  and  is 
not  always  admissible,  on  account  of  interference  with 
the  necessary  open  space  beneath. 


DEDUCTIONS. 

XVI.  We  seem  to  learn  from  what  precedes,  that : 

(1).  Since  all  heavy  bodies  not  in  motion  toward,  or 

not  approaching  the  centre  of  the  earth  (or  receding 

from  it  under  the  influence  of  previous  impulse),  exert 

a  pressure  equal    to  their  respective   weights  [vm], 

*  By  the  expression,  amount  of  action,  is  meant,  the  sum  of  products 
of  stresses  into  lengths  of  parts,  or  members. 


Two  PANEL  TRUSSES.  15 

either  directly  or  indirectly  upon  the  earth;  and,  since, 
a  body  crossing  abridge,  having  (as  bridges  are  always 
supposed  to  have),  avoid  space  underneath,  preventing 
a  direct  pressure,  it  follows,  that  every  such  body  exerts 
an  indirect  pressure  at  some  point  or  points  at  greater 
or  less  horizontal  distance  from  the  body. 

(2).  That  the  pressure  of  a  body  at  a  point  or  points 
not  directly  below  it,  can  only  take  place  through  one 
gr  more  intermediate  bodies,  or  members,  capable  of 
exerting  (by  tension  or  thrust),  one  or  more  oblique 
forces  upon  the  first  named  body,  and  it  is  the  office 
of  a  bridge  to  furnish  the  medium  of  such  horizontal 
transfer  of  pressure  [iv], 

(3.  That  a  single  oblique  force  can  not  alone  prevent 
a  heavy  body  from  falling  toward  the  earth  (since  two 
forces  can  only  be  in  equilibrio  when  acting  oppositely 
in  the  same  line),  and  that  each  oblique  force  is  equal 
to  the  combined  action  of  a  vertical  and  a  horizontal 
constituent,  of  which  the  first  alone  is  equal  to  the 
weight  sustained  and  transferred  by  the  oblique 
member,  while  the  horizontal  constituent,  acting  at 
both  extremities  of  the  oblique  medium,  must  be  coun 
teracted  by  means  outside  of  the  oblique  and  the  weight 
sustained  by  it ;  which  means  are  usually  to  be  sup 
plied  by  other  members  of  the  structure  [vni]. 

(4).  The  direct  force  exerted  by  an  oblique  member 
(in  the  direction  of  its  length),  is  equal  to  the  weight 
sustained,  multiplied  by  the  length,  and  divided  by 
the  vertical  reach  of  the  oblique,  while  the  horizonta. 
constituent  equals  the  weight  sustained  multiplied  by 
the  horizontal,  and  divided  by  the  vertical  reach  of 
the  oblique  [vn]. 

(5).  The  amount  of  material  required  in  a  tension 
member,  is  as  the  stress  multiplied  by  the  length  ot 


i6  BRIDGE  BUILDING. 

the  member  [ix]  (disregarding  extras  in  connections) 
and  the  same  is  true  of  thrust  members  of  similar 
formed  cross-sections,  sustaining  stress  proportional  to 
the  square  of  the  length  of  pieces  respectively. 

(6).  The  respective  stresses  of  two  thrust  members, 
divided  by  the  squares  of  respective  lengths,  give  quo 
tients  indicative  of,  though  not  proportional  to,  the  re 
lative  efficiency  of  material  in  the  two  members,  — the 
greater  quotient  showing  the  greater  efficiency,  or 
greater  power  of  resistance  to  the  square  inch  of  cross- 
section  [xni]. 

With  these  rules  or  principles  in  view,  we  may  pro 
ceed  advantageously  with  general  analyses  and  com 
parisons  of  different  plans,  or  systems  of  bridge  trussing, 
adapted  to  different  lengths  of  span. 


THREE  PAKEL  TRUSSES. 

XVII.  In  structures  exceeding  25  or  30  feet  in  length, 
the  length  of  joists  from  the  centre  to  the  ends,  would 
require  cross-sections  so  great,  to  give  them  the  requi 
site  stiffness,  that  their  weight  and  cost  would  become 
objectionable.  It  becomes  expedient,  then,  in  such 
cases,  to  provide  support  for  more  than  one  principal 
point,  or  transverse  beam,  or  bearer.  A  superstruct 
ure  from  30  to  40  feet  long,  may  be  constructed  with 
two  cross  beams,  supported  by  two  trusses  with  two 
pairs  of  braces  each,  with  the  feet  connected  by  a  hori 
zontal  tie  or  chord,  as  seen  in  Fig.  6. 

The  cross  beams,  may  be  at  b  bf,  or  suspended  at  c 
and  d,  at  equal  horizontal  distances  from  a  af,  and  from 
one  another;  which  latter  position  they  will  be  re- 


THREE  PANEL  TRUSSES. 


17 


garded  as  occupying  in  this  instance.  Or,  the  figure 
may  be  inverted,  thus  reversing  the  action  of  the  several 
thrust  and  tension  members. 

XVIII.  Another,  and  a  more  common  form  of  truss 
for  two  beams,  is  shown  in  Fig.  7.  These  may  be 
called  three  panel  trusses. 

PIG.  6. 


Pig.  7. 


To  compare  these  two  trusses,  suppose  the  two  to 
have  the  same  length  and  depth,  and  to  be  loaded  with 
•uniform  weights,  w,  at  the  two  points  c  and  d  in  each. 
Then,  since  we  know  from  the  principle  of  the  lever,  that 
each  weight  produces  upon  each  abutment,  a  pressure 
inversely  as  its  horizontal  distance  from  them  respec 
tively,  and  that  the  pressure  upon  the  two  abutments 
is  equal  to  the  weight  producing  it,  it  follows  that  «6, 
Fig.  6,  sustains  f  w,  and  compression  =  J  &o.  Hence 

making  ab  =  D,...  bc  —  v,  and  ac  =  h,  ...  f^w, becomes 
J  —  w,  and  multiplying  this  stress  by  length,  =  D,  and 


18  BRIDGE  BUILDING. 

changingz#toM*,wehaveforniateria]ina6,...§—  M.  But 
D*=/t'  +  v>,  whence  §^M  -  J  (7|  +  *)  M  =  (|°-f  |)M. 

Again,  abr  sustains  Jw,  with  length  =  \/4lt2~+u*,  and 
by  multiplying  and  changing  as  in  case  of  «6,  \ve  obtain 
material  in  ab1 ',  =  (-^-  4-  ~)  M,  which  added  to  amount 
for  ab,  gives  (-^  -f  i'j  M  for-  the  two  braces,  and 
(ii'  +  2v)M  for  the  four. 

The  horizontal  thrust  of  ab  =  f?r—  while  that  of  ab' 

=  i  lt-2^  =  f  wi     Hence  the  horizontal  thrust  of  ab  and 
«     «       d    D 

a6  —  £w— =  tension  of  «a',  and  material  for  chord  aa', 
equals  3  x  |— M  »— M.  Tension  of  ic  and  6W,  each, 

equals  w,  and  material  for  the  two  =  2  v  M,  which 
added  to  amount  in  aaf,  makes  the  whole  tension 
material  equal  to(—  -f2i')  M,  being  the  same  co-efficient 
of  M  as  was  obtained  for  compression. 

In  truss  Fig.  7,  ...  ab  and  a'b'  (=  D  =  v/A2  -f  v*),  evi 
dently  sustain  each  a  weight  equal  to  ?^,-and  a  stress  = 
^A2  -|-  r2  w.  Whence,  material  =  (-  +  v)  M  for  each, 

V 

and  (2-  -f  2r)  M  for  both,  while  66',  equal  to  A,  sustains 
compression  equal  to  the  horizontal  thrust  of  a6,  equal 
to—  Wj  and  requires  material  equal  to  — M,  making,  with 
amount  in  braces  ab  o'b',  (—  4-  2r)  M. 

Now  we  have  just  seen  that  the  horizontal  thrust  of 
a6,  equal  to  the  tension  of  chord  aa',  equals—  w,  and  the 


*  When  «  is  used  in  the  co-efficient  of  M,  then  M  represents  the  pr<* 
duct  of  the  stress,  in  terms  of  w,  by  length  according  to  any  assumed 
unit,  which  may  be  equal  to  v  or  not. 


THREE  PANEL  TRUSSES.  19 

length  being  3A,  the  material  consequently  equals 
—  M,  to  which  add  2rM  for  verticals,  and  we  have 

V 

(JE*!  +  2  V)M.  =»  whole  amount  of  tension  material  in 
truss  7,  which  is  less  by  n  M,  than  in  the  case  of  truss 
Fig.  6. 


XIX.  "With  regard  to  thrust  material,  it  is  clear  that 
while  in  truss  6,  the  weight  on  either  pair  of  braces,  is 
transferred  in  due  proportion  to  both  abutments,  inde 
pendently  of  the  other  braces,  whether  one  or  both  pair 
be  loaded ;  on  the  contrary,  truss  7,  when  c  only  is 
loaded,  must  transfer  $w  to  a',  which  can  only  be  done 
through  a!b',  the  only  oblique  member  acting  at  the  point 
a'.  Moreover,  the  weight  must  be  communicated  to  a'b', 
at  the  point  6',  through  the  thrust  of  bd,  and  the  tension 
ofdb',  assuming  bd  and  cb'  to  be  thrust  members.  Now, 
as  either  c,  or  d,  is  liable  to  be  loaded  with  weight  equal 
to  w,  while  the  other  is  unloaded,  it  follows  that  both 
bd  and  cb'  are  liable  to  sustain  weight  equal  to  $w,  and 
require  thrust  material  equal  to  j(—  -f  v)  M  for  each, 

A  or  (2nh*  -f  ^-)M  for  the  two.     The  whole  amount  of 

x  do  o  ' 

thrust  material  for  truss  7,  then,  equals(—  -f  2  T)M, 
(the  amount  found  above)  +  (?~  -f  }t?)]C,  equal  to 
(W  +  2  §  v)  M,  against  (—  -f  SI?)M  for  truss  6;  the 
difference  being  pffl  —  jry  M.  If  this  be  a  positive 

quantity,  the  balance  is  in  favor  of  truss  7,  and  if  nega 
tive,  in  favor  of  tress  6,  as  regards  amount  of  action 

on  thrust  material;  while,  if  i^-  : —  \  v  =  zero,  the 
amount  of  thrust  action  is  the  same  in  both  trusses. 


20  BRIDGE  BUILDING. 

Either  of  these  suppositions  may  be  true,  according  to 
the  relative  values  of  A  and  v.     If  h  =  tV2, 


If    h,   be    greater  than   iV2  —  J-  —  -  fv     is 


positive,  and  if  A  be  less  than  v\/2,  the  value  is  nega 
tive.  But  the  amount  is  trifling  in  any  probable  rela 
tion  of  A  and  i',  and  may  be  disregarded  in  this  general 
comparison. 

Calling  then,  the  amount  of  action  upon  thrust  mate 
rial  in  the  two  plans  equal,  there  is  a  probable  advan 
tage  in  favor  of  truss  7,  as  to  efficiency  of  thrust 
material,  while  the  latter  truss,  shows  a  positive  advan 
tage  over  truss  6  in  amount  of  tension  material,  equal 
to  (™  +  2i?)  —  f-^-2  +  2i?)  M  =  *'  M.  This  is  equal  to 

x    1)  x    -0  V 

4M,  when  h  •=  2v  —  2  ;  which  is  in  tolerable  proportion 
for  the  trusses  under  discussion,  and,  substituting  these 
values  of  h  and  v  in  the  expressions  of  tension  material 
in  the  trusses  respectively,  we  have  (16  -f  2)M  for  truss 
6,  and  (12  -f  2)M  for  truss  7,  being  about  28J  per  cent 
more  for  6  than  for  7. 

The  same  difference  would  appear  with  Fig.  6  in 
verted,  the  thrust  and  tension  action  being  the  same 
in  amount  of  each,  only  sustained  by  different  mem 
bers,  thrust  members  in  one  case  becoming  tension 
members  in  the  other. 


FIVE  PAKEL  TRUSSES. 

XX.  Truss  Fig.  7,  may  be  increased  in  length  and 
number  of  panels,  by  introducing  additional  panels 
between  the  end  triangular  panels,  and  the  rectangular 
centre  one  either  of  an  oblique  form,  as  in  Fig.  8,  which 
represents  an  arch-truss,  or  of  a  rectangular  form  as  in 


FIVE  PANEL-  TRUSSES. 


21 


Fig.  10.  The  truss  on  the  plan  of  Fig.  6,  may  be 
lengthened  by  introducing  additional  pairs  of  inde 
pendent  braces,  as  seen  in  Fig.  9. 


For  the  analysis  of  these  trusses,  using  the  same  no 
tation  as  before,  as  far  as  applicable,  that  is,  making 
v  =  verticals  ck,  in  8  and  10,  and  equal  to  nn',  pmf,  etc., 
in  Fig.  9  ;  h  =  ab,—  width  of  panel  in  each  figure,  =  J 
whole  chord  ;  w~ uniform  weights  at  the  four  bearing 
points  in  each,  and  M  =  weight  of  material  required  to 
sustain  a  stress  equal  to  w,  with  length  equal  to  1 ; 
then,  making  Ib  =  §  v  in  truss  8,  it  is  obvious  that  the 
two  abutments  at  a  and /together  sustain  4iv,  with  the 
common  centre  of  gravity  of  all  the  weights  midway 
between  abutments,  whence  each  abutment  sustains 
2w,  equal  to  weight  sustained  by  al.  The  compression 
of  al  therefore  equals  %£w.  But  al  =  </h2+ %v'\ 
which  substituted  in  last  preceding  expression,  gives 
|  v'/i2  4-  J  vzWj= compression  of  al.  Whence,  multiply- 

V  

ing  by  length,  \/A2-f  jy2,   and   changing  w   to   M,   we 
have   (— H-lJv)  M  =  material  for  al. 

The    horizontal    thrust    of    al,    [xvi    (4)]     equals 

2  10  —  =  —w,  =  tension  of  chord  af. 

|D  v 

The  oblique  member  Ik,  sustains  weight=w  (through 
the  vertical  cA-*  and  has  a  vertical  reach  =  Jv, 


22  BRIDGE  BUILDING. 

whence  it  suffers  compression  equal  to^j  w,  =*^iw,  =» 
3  ^A2  4-  jv2w,  and  requires  material  equal  to  (—  + 

9 

!I')M,  while  its  horizontal  thrust  equals  -£-w,  •*l*t0,«i 
compression  of  ki,  by  which  it  is  contracted.  The  ma- 

O7  9 

terial  required  for  ki,  therefore,  =  — M.    Material  lor  ig 

and  gf,  is  the  same  as  above  found  for  al  and  Ik,  and, 
doubling  those  quantities,  and  adding  amount  just 
found  for  ki,  we  obtain( — .  -f  3|v)  M,  -=  material  in 
the  whole  arch. 

The  tension  of  the  chord  af  (Fig.  8),  has  been  seen 
to  be  equal  to  3—  wy  whence,  multiplying  by  the  length, 

5h,  and  changing  w  to  M,  we  have  !5?M,*=  material  for 
chord. 

The  4  verticals  sustain  each,  weight  =  w,  and  the 
aggregate  length  being  3Ji>,...  material  =  3 JVM.  This, 
added  to  amount  in  chord,  gives  (—  4-  3Jv)M,  —  ten 
sion  material  required  to  support  a  full  uniform  load, 
as  above  assumed.  But  since  any  number  of  the  points 
t),  c,  dj  e,  are  liable  to  be  loaded  while  the  others  are 
unloaded,  it  is  obvious  that  in  such  case,  the  arch  will 
not  be  in  equilibria,  the  loaded  points  tending  to  be 
depressed,  while  the  unloaded,  tend  to  be  thrust  up 
ward.  Hence  the  arch  requires  the  action  of  the  ob 
liques,  or  diagonals,  in  the  three  quadrangular  panels,  to 
counteract  such  tendency ;  and,  as  will  appear  further 
on,  these  members  will  require  material  equal  to  about 
one-third  of  the  amount  required  in  the  chord,  thus  in 
creasing  the  amount  of  tension  material  for  the  truss  to 


FIVE  PANEL  TRUSSES.  23 

XXI.  In  truss  Fig.  9,  each  brace  obviously  sustains 
a  portion,  x,  of  the  weight  w,  which  is  to  ?.0,  as  the 
horizontal  reach  of  its  antagonist,  as  to  horizontal 
action,  or  its  fellow  and  assistant  vertically,  is  to  the 
whole  length  of  chord ;  that  is,  the  weight  x,  bearing 
at  m,  through  mnf,  is  to  w,  as  ns  to  ms ;  or,  x :  w  : :  4  :  5. 
Hence  x  =  $w.  This,  multiplied  by  the  horizontal 
reach,  equal  to  A,  and  divided  by  v,  gives  the  horizontal 

thrust  of  the  brace,  equal  to  %-w. 

FIG   9. 
71' 


n 


In  like  manner,  mmf  sustains  a  weight  x',  which  is  to 
w,  asps  to  ms,  i.  e.,  x'  :  w  :  :  3  :  5,  whence  x1  =  |M>,  and 
the  horizontal  thrust  =  -|  2—w  =*  §-«>;  and  in  general, 

the  horizontal  thrust  of  a  brace  in  this  kind  of  truss, 
equals  w,  multiplied  by  the  product  of  the  number  of 
sections  of  chord  at  the  right  and  the  left  of  the  point  of 
application  (of  the  weight),  and  divided  by  the  whole 
number  of  chord-sections,  and,  by  the  vertical  reach  (v) 
of  the  brace. 

But  the  horizontal  thrust  of  mn'  equals  that  of  n's,  = 
that  of  mt  ,and  the  horizontal  thrust  of  mm',  equals  that 
of  m's  —  that  of  mu,  whence,  horizontal  thrust  of  the 
4  braces  bearing  at  m,  equals  twice  that  of  mn'  and 

mm'  together,  =  2(4^  +  1-)^  =  ^w  =  4*w.  This 

/O  /  \  O        m  O    n     /  .R  j.  m 


24  BRIDGE  BUILDING. 

being  equal  to  the  tension  of  the  chord,  multiplying 
by  length  5A,  and  changing  w  to  M,  gives  material  for 
chord  =  —V  Adding  to  this,  4fM,  for  4  verticals 
with  stress  =  w,  and  length  =  v,  each,  makes  whole 
amount  of  tension  material  equal  to  (—  +4vJM,  being 
very  nearly  the  same  as  for  truss,  Fig.  8. 

XXII.  As  for  braces  in  truss  9,  we  have  already 
seen  that  each  brace  sustains  weight  equal  to  w,  multi- 
tiplied  by  the  number  of  panels  crossed  by  its  fellow, 
and  divided  by  the  number  of  panels  in  the  whole 
truss.  Hence  mnf  sustains  |i#,  with  length  equal  to 

\/A2-fy2.     Therefore,  stress  =  f  \/  A2  +v'2iv,  which   mul- 

c 
tiplied  by  length,  and  w  changed  to  M,  gives  material 

for   mn'=  j(-+0)M»  =»  (4    +  -$-)M.       mm'    sustains 


f  ?0   with    length   =  V4/i2  +  v2,    whence    material  = 
I  (4^1+0  }Mj  =(^.9-f.^L)M.    mu  sustains  §M?  with  length 

-%/9/iHv2,  and  material  equals  (^+~-)M,  while  mt, 

sustains    Jw,    with     length  =   \/16A2+y2     requiring 
material  =  (^  +  |-)M.     Then,  adding  and  doubling 

these  amounts,  we   obtain(—  +40)lf,  against  (—  2  -j- 

3Ju)M,  for  truss  8  ;  a  difference  of  about  30.6  per  cent 
when  h  =  v,  and  about  32.6  per  cent  when  h  =*  2v. 

Thus,  truss  Fig.  8  has  over  30  per  cent  advantage 
over  truss  Fig.  9,  in  the  economy  of  amount  of  action 
upon  thrust  material,  with  the  advantage  as  to  efficiency 
of  action  of  this  material,  undoubtedly,  also  on  the  side 
of  truss  8.  Tension  material  is  nearly  the  same  in 
both. 


FIVE  PANEL  TRUSSES. 


25 


XXIII.  If  truss  Fig.  9  be  inverted,  dropping  the  ob 
lique  members  below  the  road-way  of  the  bridge,  thus 
reversing  the  action  of  thrust  and  tension  members,  the 
thrust  material  would  act  with  nearly  equal  advantage 
in  both  plans,  and  with  about  the  same  amount  of 
action.  But  the  30  per  cent  advantage  as  to  amount 
of  action  upon  tension  material,  would  still  be  in  favor 
truss  8.  Besides,  it  is  only  in  exceptional  cases  that 
this  arrangement  can  be  adopted,  on  account  of  interfer 
ence  with  the  necessary  space  below  the  bridge. 


XXIV.  In  truss  Fig.  10,  suppose  the  points  6,  c,  d,  e, 
to  be  loaded  successively  from  left  to  right,  with  uni 
form  weights  equal  to  w  each,  and  suppose  the  truss  to 
be  without  weight,  as  we  have  hitherto  done.  When  b 
alone  is  loaded,  \w  must  bear  at  /,  [xvm]  which  may 
be  effected,  either  by  tension  of  bl,  thrust  of  Ic,  tension 
of  ck,  thrust  of  kd,  &c.,  by  tension  vertical  and  thrust 
diagonal  alternately,  till  it  reaches  /;  acting  in  its 
course  upon  4  verticals,  and  4  obliques,  with  a  weight 
upon  each,  equal  to  ^w.  Or,  the  weight  maybe  trans 
ferred  by  tension  of  bk,  ci  and  dg,  and  thrust  of  kc,  id 
and  gf.  These  alternatives  are  subject  to  the  control 
of  the  builder,  and  he  will  form  and  connect  the  parts 
accordingly.  Let  it  be  assumed  that  the  truss  has  ten 
sion  diagonals,  and  thrust  uprights  at  c  and  d,  while  M 


26  BRIDGE  BUILDING. 

and  eg  are  necessarily  tension  members  in  all  cases,  in 
practice. 

Again  a  weight,  w,  at  c,  must  cause  pressure  equal 
to  f  w  at/,  through  tension  of  ci  and  dg,  and  thrust  of  id 
and  gf.  This,  with  the  ^w,  from  the  weight  at  b,  makes 
$w,  acting  on  ci.  But  the  weight  at  c,  causes  pressure 
equal  to  f?0  at  a,  necessarily  through  tension  of  cl; 
and  since  c£  and  bk  are  antagonistic,  the  action  upon 
one  tending  to  produce  relaxation  of  the  other,  it  fol 
lows  that  only  one  can  act  at  the  same  time,  unless 
unduly  strained  in  the  adjustment  of  the  truss.  Hence, 
the  ^w,  which  acts  upon  bk,  when  b  alone  is  loaded,  is 
overbalanced  by  the  f  w,  tending  to  act  upon  cl,  on 
account  of  the  load  at  c ;  and  the  result  is,  that  bk  is 
relaxed,  the  whole  weight  at  b,  is  necessarily  sustained 
by  bl  and  la,  and  the  {10,  which  must  by  a  statical 
necessity,  bear  at/,  in  consequence  of  the  loads  at  b 
and  c,  is  all  made  up  from  the  weight  at  c,  leaving  only 
f  (jo  of  this  weight  to  bear  at  a,  through  cl.  Now,  since 
it  is  obvious  that  all  load  at  c,  d,  or  e,  must  contribute 
to  the  pressure  at  «,  which  can  only  occur  through 
action  upon  c?,  it  follows  that  bk  can  only  sustain  the 
whole  weight  of  \w,  when  the  point  b  alone  is  loaded ; 
and  consequently,  that  ^w  is  the  greatest  weight  that 
bk  can  ever  be  subjected  to. 

Then,  applying  another  weight,  w,  at  d,  it  must  add 
f  10  to  the  pressure  at/,  through  tension  of  dg  and  thrust 
of  gf;  which  last  amount,  added  to  f  10,  communicated 
to  dg  through  ci  and  id,  makes  f  w,  as  the  weight  sus 
tained  by  dg.  But  the  weight  at  d,  also  causes  pres 
sure  at  a,  equal  to  §10,  which  can  only  be  done  through 
action,  or  tendency  to  action  upon  dk,  and  since  dk  and 
ci  are  antagonists,  only  one  can  act  at  once,  and  that, 
only  with  a  force  equal  to  the  excess  of  tendency  to 


FIVE  PANEL  TRUSSES.  27 

action  of  the  one,  over  that  of  the  other.  Now  we 
have  seen  that  weights  at  b  and  c,  tend  to  throw  \w 
upon  ci,  while  the  weight  at  d,  tends  to  throw  f  ?0  upon 
dk.  Hence,  in  these  circumstances,  ci  only  sustains 
JMJ,  which  is  transferred  to  dg  through  thrust  of  id, 
while  dk  is  relaxed,  and  the  whole  weight  at  d,  is  sus 
tained  by  dg;  making,  with  the  \w  from  ci,  just  above 
mentioned,  $w,  equal  to  the  pressure  due  upon  the 
abutment  at/,  on  account  of  weights  at  b,  c  and  d. 

Lastly,  a  weight,  w,  at  e,  tends  to  give  pressure  equal 
to  \w  at/,  through  eg  Sindgf,  and  a  pressure  equal  to  £ 
w  at  a,  through  ei,  dk,  etc.  This  latter  tendency  has 
the  effect  to  diminish  by  ^w,  the  tendency  of  previously 
imposed  weights,  to  throw  f  10  upon  dg,  reducing  it  to 
f  10,  and  to  neutralize  the  balance  of  ±w  acting  upon 
ci,  after  the  imposition  of  the  weight  at  d,  leaving  c\ 
and  dk  both  inactive,  while  eg  sustains  the  whole  weight 
applied  at  c,  equal  to  w. 

Now,  as  we  have  seen,  any  weight  at  d  or  e,  tends  to 
throw  action  upon  dk,  thereby  diminishing  action  upon 
ci,  and  since  weight  at  b  and  c,  both  contribute  to  the 
stress  of  ci,  it  follows  that  the  maximum  action  upon 
ci,  occurs  when  b  and  c  are  loaded,  and  d  and  e,  unloaded. 

For  similar  reasons,  the  maximum  action  upon  dg,  oc 
curs  when  e  alone  is  unloaded. 

The  maximum  weight  sustained  by  Ib,  and  eg,  is  the 
weight  applied  directly  at  each  of  the  points  b  and  e, 
equal  to  w,  and  the  maximum  weights  sustained  by  ei, 
dk,  and  cl,  are  the  same  as  those  sustained  by  bk,  ci  and 
dg,  each  respectively,  as  just  above  determined  ;  while 
al  and  gf,  both  receiving  action  from  weight  on  any 
part  of  the  trass,  obviously  sustain  their  maximum 
weight,  equal  to  Zw,  under  the  full  load  of  the  truss. 


28  BRIDGE  BUILDING. 

The  section  ab,  of  the  lower  chord,  suffers  a  stress 
equal  to  the  horizontal  thrust  of  al,  which  of  course, 
is  greatest  vtkenal  sustains  the  greatest  weight.  This 
has  just  been  seen  to  be  equal  to  2w,  and  occurs  under 
a  full  load  of  the  truss.  Hence  the  greatest  stress  upon 

ab  equals  2w  — ,  and  is  communicated  without  change 

to  be,  bk  being  inactive  when  the  truss  is  fully  loaded. 
The  section  cd,  suffers  stress  equal  to  the  combined 
horizontal  action  of  al  and  Ic,  which  must  be  greatest 
when  this  combined  action  is  greatest.  That  is  also 
under  the  full  load  of  the  truss.  For,  though  Ic  sus 
tains  J?0  more  weight  when  b  is  unloaded,  the  same 
cause  relieves  al  of  the  amount  of  %w.  Consequently, 
the  weight  borne  by  the  two,  is  Ji0  less  in  this  case, 
than  when  the  truss  is  fully  loaded.  The  greatest  com 
bined  weights,  then  sustained  by  al  and  Ic9  being  equal 
to  3w,  the  greatest  stress  of  cd  equals  3w  — .  This  is 

also  the  greatest  compression  suffered  by  the  upper 
chord  Ig,  since  the  latter  is  also  equal  to  the  combined 
horizontal  thrust  and  pull  of  al  and  Ic.  The  stress  of 
this  chord  is  the  same  throughout,  because  the  obliques 
meeting  at  k  and  i,  are  inactive  when  the  truss  is 
loaded  throughout. 

The  maximum  compression  upon  ck  and  id,  equals 
the  greatest  weight  sustained  by  d  and  die,  already  found 
to  be  equal  to  f  w. 

XXV.  Having  thus  ascertained  the  greatest  weights 
sustained  by  the  several  oblique  members,  and  the 
greatest  stresses  of  the  horizontals  and  verticals,  we 
may  deduce  the  required  amount  of  material,  or,  per 
haps  more  properly,  the  amount  of  action  upon  the  ma 
terial  required  for  the  truss,  as  compared  with  like 


FIVE  PANEL  TRUSSES.  29 

amount  of   action  in    trusses    8  and   9,  thus  :    Max. 
weight  on  end  braces,  2w  x  length  v/  A2  -f-  v*  -•  stress  = 


Hence,  action  upon  material  for  the      ,  A75 
tvvo=   ...................................      (£+' 

Max.  weight  on  2  verticals  =  f  10  x 

length  of  the  two  (=*  20),  gives  ......  I 

Max.  stress  of  upper  chord  =  810- 

X  length   (  =  3A),   gives  amount  ^ 

of  action  =  ..............................         ^  9 

Making  total  amount  of  action   on 

thrust  material  =  .....................       -5-         slv  M 

Aggregate  max.  weight  on  6  tension 
diagonals  =  2£w=4w.  This  by  the 
length  (  =  v/A2  -f  y2),  gives  stress 
=  4  w\/h?  +  ga  ;  whence  amount 

of  action  on  material,  equals  ......      t"f~  "^   4v/M- 

2  tension  verticals  sustain  each,  lw, 

with  length  =«  u,  giving  amount  of 

action  for  the  two  =  .................  2v  M. 

Stress  of  middle  section,  lower  chord 

=  3w-,  X  length  (  =  A),    gives 

Q  ^'w 

action  ....................................         d  0   • 

4  remaining  sections,  with  stress  = 

2u?4  X  length  (  =  4A),  give  ..........        87^M. 


Making  whole  amount  of  action  on      ,    ^ 
tension  material  =   .  >    u  ~*~ 


so 


BRIDGE  BUILDING. 


SYNOPTICAL  STATEMENT  IN  REGARD  TO  TRUSSES  (Figs. 
8,  9  and  10. 


£ 

B 

0 

to 

fc 

0 

H 
M 
M 

AMOUNT  OF  ACTION  UPON  MATERIALS 

B 

^0 

H 

"*~ 

Tension. 

Compression. 

TfcoT 

Q 

XX 

(  207*'  _L4it,)  M 

(  w?  +  3^r)  M 

/35^a     ,     rr£v\  M 

9 

XXI 
XXII 

,20A'  +1,)M 

(  207,'     ,    4  )  M 

(J^l  +  8v  )  ii 

^    v 

\                     -x  i/  y   AI 

10 

(         ~{~  Qv  )  M 

V     v 

/  28/«a    i    1  1  j    \  _. 

V    „            I/ 

Making    A  =  y  «*  1,    the    above   table  will  be  as 
follows : 

8 24JM  18JM 42fM 

9 24M 24M  48M 

10 2lM 18JM 39JM 


XXVI.  This  shows  very  nearly  the  relative  amount 
of  tension  material  required  in  the  several  plans; 
while,  as  previously  stated,  the  amount  of  compression 
material  is  not  so  nearly  indicated  by  the  figures  and 
expressions  giving  the  amount  of  action  (sum  of  stresses 
into  lengths  of  pieces),  as  in  case  of  tension  members. 
The  compression  material  in  No.  8  (the  arch  truss),  is 
undoubtedly  more  efficient  in  action  than  in  either  of  the 
others,  while  that  in  No.  9,  is  unquestionably  the  least 
so.  In  fact,  this  truss  will  be  hardly  considered  as 
possessing  advantages  of  any  kind,  sufficient  to  induce 


THE  ARCH  TRUSS.  31 

its  adoption  ;  and  it  will  not  be  considered  in  the  dis 
cussions  and  comparisons  in  regard  to  trusses  of  greater 
span,  to  which  we  may  now  proceed. 


TRUSSES  WITH  SEVEN  PANELS. 
THE  ARCH  TRUSS. 

XXTII.  In  Fig.  11,  let  md  -  i>,  and  h-  ab  =-£.  If 
each  of  the  points  6,  c,  d,  etc.,  be  loaded  with  a  weight 
equal  to  w,  then,  in  order  that  the  arch  may  be  in  equi- 
librio  under  the  effects  of  these  weights,  without  any 
action  of  the  diagonals,  it  is  necessary  that  each  section 
of  the  arch  have  the  same  horizontal  thrust,  since,  if 
one  section  have  a  greater  horizontal  thrust  than  the 
one  opposed  to  it  at  either  end,  the  diagonals  alone  can 
sustain  the  surplus.  And,  that  the  sections  may  have 
the  same  horizontal  thrust  each  must  have  a  vertical 
reach  (the  horizontal  reach  being  the  same  for  all), 
proportional  to;the  weight  (W)  sustained  by  each.  For 
illustration,  horizontal  thrust  being  equal  to  W— ,  in 
order  that  this  expression  may  represent  a  constant 
quantity,  h  remaining  constant,  v  must  be  as  W. 

Now,  ml  being  horizontal,  can  sustain  none  of  the 
weight  acting  at  the  point  w,  through  the  vertical  md; 
hence  mn  must  sustain  a  weight  equal  to  w.  This  is 
transferred  to  no  [vm],  and  in  addition  to  the  weight 
at  c,  makes  2w  sustained  by  no.  The  latter  weight  is 
in  turn  transferred  to  <xz,  and,  in  addition  to  the  weight 
at  6,  makes  8w,  to  be  sustained  by  ao.  The  vertical 
reaches,  therefore,  beginning  with  aot  should  be  as  3, 
2  and  1 ;  whence,  ob  should  equal  Jy,  and  no  should 
equal  ft'. 


32  BRIDGE  BUILDING. 

The   thrust  of  ao,  then,  equals   3i0-2£,  =  610-??., 
6w  \/^!±V  ;  whence,  amount  of  action 


on  material*  =  ..............................  (?£.  -f  IJvJxM. 

Thrust  of  on,  =  2i<;  ™    =  6^-^-,  = 
_  f«  « 

6w?  %/4!±i*!,  and  material  =  ........  .  ......  (?^  +  t«?}xM. 

i)  v  •« 

Thrust  of  wm  =u;S  =  610^  = 
_  i»  « 

6u?  ^^±^!,  and  material  ==  ......         ,..(—  +  IV}XM. 

V  ^    V  b     ' 

Thrust  of  ml  (=  horizontal  thrust 
of  nm),  =-  ^-4-=  6^|,  and  material  =  ..............  6-XM. 

Adding  these  amounts,  and  repeating  the  first  three, 
we  have  (i^L  -f  4fv)xM,  equal  to  amount  of  action 
upon  the  arch  when  fully  loaded. 


/        y 

The  stress  of  the  chord  obviously  equals  the  horizon 
tal  thrust  of  ao.  equal  to  3^—.  =  6w— ;  and  is  the  same 

1«  t 

throughout,  when  the  truss  is  fully  loaded  throughout. 
Hence,  for  the  whole  chord,  we  have,  stress  =  6w— 
multiplied  by  length  (=  7A),  and  w  changed  to  M, 
=  42— XM,  representing  the  material  required  for  the 
chord. 

The  above  are  assumed,  for  the  present,  to  be  the 
greatest  stresses  that  any  part  of  the  chord  or  arch  can 

*  By  amount  of  action  upon  material,  is  meant  the  stress  of  a  member 
multiplied  by  its  length. 


SEVEN  PANEL  TRUSSES.  33 

be  subjected  to,  in  any  condition  of  the  lond  ;  ?0,  being 
the  maximum  weight  for  any  one  of  the  sustaining 
points,  b,  e,  d,  &c.  This  is  a  point  we  shall  be  better 
enabled  to  verify  after  considering  the 

STRESSES  OF  VERTICALS  AND  DIAGONALS. 

XXVIII.  As  the  diagonals  do  not  act  under  a  full 
load  of  the  truss,  the  verticals  must  each  sustain  a  ten 
sion  equal  to  10,  when  the  weights  are  applied  at  the 
chord  ;  and,  the  diagonals  acting  by  tension,  serve, 
when  in  action,  to  diminish  the  tension  of  verticals,  or 
to  subject  them  to  compression,  but  can  never  increase 
their  action  of  tension.  Hence,  the  maximum  tension; 
stress  of  each  vertical  equals  w. 

In  order  to  bring  the  diagonals  into  action,  the  truss 
must  obviously  be  unequally  loaded  ;  and,  to  determine 
the  maximum  stresses  of  the  several  diagonals  respec 
tively,  we  may  begin  by  removing  the  Weight  at#  ;  (see 
Fig.  11  A),  and,  to  facilitate  the  process,  let  10"  represent 
ic  divided  by  the  number  of  panels  in  the  truss  (=  7  in 
this  case),  i.  e.,  ID"  =  }w.  Then,  the  full  load  of  the 
truss  bearing  with  a  weight  of  810,  =21i0",  at  i,  ...  with 
load  removed  from  g,  the  bearing  at  z,  equals  2J.10"  — 
6*0",  =  ~L5w"  ;  and  produces  a  thrust  upon  ij  equal  to 
/^!±i!i.  Then,  taking^  by  any  convenient  scale, 


on  ij  produced,  to  represent  the  thrust  of  ij  (reduced  to 
wn  with  a  numerical  coefficient,  according  to  the  pro 
portions  of  the  truss),  and  drawing  qr  parallel  with  fj, 
and  meeting  jk  produced  in  r,  it  is  obvious  that  the 
three  forces  acting  alj,  namely,  the  thrust  of  ij  and  J/c, 
and  the  tension  of  fj,  will  be  represented  respectively 
by  the  sides  of  the  triangle  jqry  parallel  respectively 
with  the  directions  of  those  forces;  and  may  be  mea- 
5 


34 


BRIDGE  BUILDING. 


sured  by  scale  and  di 
viders,  or  calculated  tri- 
gonometrically. 

Now,  it  will  be  seen 
taatthegreaterthe  pres 
sure  at  i,  the  greater 
the  thrust  of  ij,  repre 
sented  by  j<?,  and  conse 
quently,  the  greater  the 
line  qr,  representing  the 
tension  of  fj.  But  the 
pressure  at  i,  is  mani 
festly  the  greatest  pos 
sible  in  the  case  here 
supposed,  except  when 
the  weight  at g is  wholly 
or  partially  restored,  in 
which  case  the  tension 
of  fj  would  be  wholly 
or  partially  relieved. 
Hence,  it  follows  that 
the  maximum  stress  of 
jO'i  occurs  when  all  the 
supporting  points  ex 
cept  #,  have  their  full 
load,  and  the  point  g  is 
without  load. 

Taking,  then,  fs  — 
qr,  and  drawing  si  par 
allel  with  #/,  st  will  re 
present  the  horizontal, 
and//',  the  vertical  effect 
(equal  to  3wr")  of  the 
action  of  fj ;  the  former 


SEVEN  PANEL  TRUSSES.  35 

effect  being,  in  addition  to  the  tension  of  / 1,  resisted 
by  the  tension  of  ef,  while  the  latter  is  counteracted 
by  the  weight  at  /,  and  the  tension  of  fk  is  thereby 
diminished,  but  not  exhausted*.  But  if  the  weights 
were  applied  at  the  arch  instead  of  the  chord,  then  /&, 
in  this  condition,  would  suffer  compression  represented 

by/<- 

XXIX.  If  the  points  g  and/  be  unloaded,  the  pres 
sure  at  i  is  reduced  to  lOw",  and  the  thrust  of  ij  =  Ww" 
v/^-H^  Then,  taking  jq'  by  the  scale,  to  represent 

this  quantity,  and  drawing  q'r'  parallel  withjf),  #'r/» 
compared  with  the  same  scale,  will  give  the  stress  of 
fj;  from  which,  as  in  the  preceding  case,  we. obtain. 
ft'  (  =  2*0"t),  to  represent  the  vertical  effect  of  the  ac 
tion  of  fj  ;  and,  there  being  no  weight  at  /,  this  force 

*  Since  the  vertical  reach  of  jk  is  £  that  of  ij,  and  their  vertical  ac 
tions  (horizontal  thrust,  and  horizontal  reach  being  the  same),  as  their 
respective  vertical  reaches,^  must  react  downward  at,;,  with  £  of  the 
lifting  force  exerted  by  ij.  Then,  if  a  weight  be  suspended  at  g,  by 
the  vertical  jg,  equal  to  £  of  the  weight  bearing  at  i,  the  forces  acting 
at  j,  through  ij,  jk,  and  jg,  are  in  equilibrio.  But  if  the  weight  at  g 
be  less  than  ^  of  the  pressure  at  i,  the  tendency  of  the  pointj  is  upward, 
and  exerts  a  lifting  force  upon  fj,.  But  the  action  of  fj,  brings  into 
play  horizontal  reaction  injk,  equal  to  that  of  fj,  which  gives  jk  a  de 
pressing  action  at  j,  equal  to  f  o!  the  lift  ot'jy.  This  depressing  power 
of  jk,  depends  on  forces  acting  directly  or  indirectly  at  k,  and  which 
go  to  make  up  part  of  the  pressure  at  i.  Hence,  jk  supports  at  the 
upper  end,  at  k,  first,  f  of  the  weight  bearing  at  i,  in  virtue  of  the 
horizontal  thrust  received  through  ij,  and  second,  f  of  the  other  £ 
(when  there  is  no  weight  at  g),  in  virtue  of  the  horizontal  thrust  com 
municated  through^)'.  Now,  g  being  alone  unloaded,  the  bearing  at 
i  is  I5w",  of  which,  K\wH  is  received  through  jk,  in  virtue  of  horizontal 
thrust  counteracted  by  ij.  and  \  of  the  other  5w",  in  virtue  of  horizontal 
thrust  counteracted  by  fj,  in  cons'-quence  of  the  latter  sustaining  fof 
said  5w".  Hence,  fj  sustains  T\  or  |,  while  jk  sustains  |f,  or  |  of  all 
the  weight  bearing  at  i,  when  g  alone  is  unloaded  ;  and  3w",  therefore, 
is  the  maximum  weight  sustained  byfj. 

f  Since  jq  represents  the  action  of  ij,  due  to  a  pressure  of  15?£"  at  i, 
and  jq' ,  tlie  action  of  ij,  due  to  a  pressure  of  Ww",  it  follows  that  jq' 
=  iU<7  ;  whence  q'r'  obviously  equals  £  qr,  and/s'  =-&/*•  Consequently, 
ft'  =  •){/£.  But  ft  represents  the  lift  of  fj,  =  3*0",  whence  ft'  repre 
sents  2w". 


36  BRIDGE  BUILDING. 

is  expended  in  causing  compression  upon  fk ;  and  is 
the  measure  of  the  greatest  compression  that  member 
can  receive  through  fj.  But  fk  is  also  liable  to  com 
pression,  or  a  tendency  thereto,  from  the  tension  offl 
when  /  and  g,  are  loaded,  or  g  alone,  and  the  other 
parts  unloaded.  This,  however,  in  the  former  case, 
will  never  equal  the  weight  at  /",  and  in  the  latter,  the 
compression  will  not  exceed  that  just  found,  resulting 
from  action  of  fj ;  as  will  be  better  understood  here 
after. 

Now,  asjr'  represents  the  thrust  ofj&,  if  we  take  kv, 
on  jk  produced,  equal  tojrf, —  raise  the  vertical  vx  — 
ft',  and  join  kx9  the  line  kx  represents  the  resultant  of 
the  forces  kv  and  ft  (representing  thrust  of  jk  and/A:) ; 
and  xy,  drawn  parallel  with  ke,  represents  the  tension 
of  ke  ;*  This  is  the  maximum  stress  of  the  diagonal  ke. 

XXX.  For,  when  the  left  half  of  the  truss  has  more 
load  than  the  left  hand  abutment  is  required  by  the 
statical  law  to  sustain,  it  is  clear  that  a  part  of  the 
weight  on  the  left,  is  transferred  from  left  to  right  past 
the  centre  through  dl;  that  being  the  only  member 
capable  of  effecting  the  transfer.  It  is  also  clear,  that 
such  transferred  weight,  together  with  the  weight  at  e, 
if  any,  is  sustained  by  Ik  and  ek,  and  causes  pressure 
at  i,  equal  to  the  weight  sustained  by  Ik  and  ek.  Also, 
that  this  pressure  at  i9  causes  a  horizontal  thrust  in  ij, 
which  is  all  transferred  to  Ik  (except  when  kg  is  in  ac 
tion),  and  gives  a  lifting  power  to  Ik,  equal  to  J  of  that 
exerted  by  ij  (the  vertical  reach  of  the  former  being  J 
that  of  the  latter),  that  is,  equal  to  J  of  the  weight 

*  The  sides  of  the  triangle  kxy,  being  parallel  with  the  directions 
of  the  thrust  of  Ik,  the  tension  of  ek,  and  the  resultant  kx,  of  the 
thrust  ofjk  and  fk,  which  4  forces  are  in  equilibrio  at  the  point  k. 


SEVEN  PANEL  TRUSSES.  37 

transferred  by  Ik  and  ek  together.  But  the  lifting 
power  of  Ik  is  further  increased  by  J  of  the  weight  sus 
tained  byjf)',  which  increases  the  horizontal  thrust  of 
Ik,  the  same  as  a  like  amount  sustained  by  ij ;  also,  by 
J  the  weight  sustained  by  ek ;  this  member  having  5 
times  the  vertical  reach  of  Ik.  Now,  as  each  one  of 
these  items  results  from  the  weight  transferred  through 
Ik  and  ek,  and  is  greater  or  less  in  proportion  as  the 
last  named  weight  is  greater  or  less  (/and  g  being  un 
loaded),  since  all  the  conditions  are  the  same,  except 
as  to  amount  of  weight,  it  must  follow  that  the  greatest 
stress  of  ek,  is  when/  and  g  are  unloaded,  and  all  the 
other  points  b,  c,  &c.,  are  fully  loaded  —  unless  it  be 
when  /  and  g,  or  one  of  them,  be  wholly  or  partially 
loaded.  But  any  weight  at/,  increases  the  thrust  and 
lifting  power  of  Ik,  through  increased  action  of  ij  and 
fj  both,  while  it  diminishes  the  amount  sustained  by 
ek  and  Ik,  whence  the  action  of  ek,  is  diminished,  inas- 
Vnuch  as  it  transfers  to  k,  a  less  proportion  of  a  less 
weight. 

Again,  weight  applied  &t  g,  while/  is  unloaded,  re 
lieves  the  tension  of  fj,  and  diminishes  its  lifting  power 
represented  by/C  and  vx,  and  if  of  sufficient  amount, 
relaxes  fj,  and  brings  tension  upon  gk;  so  that,  when 
the  weight  at  g  equals  w,  or  7w",  Ik  has  a  lifting  power 
=  J  pressure  at  i,  less  what  is  due  to  the  horizontal  pull 
of  gk,  plus,  amount  due  to  horizontal  pull  of  ek;  while 
the  weight  bearing  at  k,  equals  9w"  (being  weight  at 
e  (=  1w")  -f  2i0"  through  dl).  Now  if  ek  lifts  as  much 
as  kg,  Ik  must  have  as  great  a  horizontal  thrust  as  ij, 
and  be  capable  of  lifting  J  16w"  (=  weight  bearing  at 
i)9  =5ji0"  ;  which  taken  from  9w"  bearing  at  k,  leaves 
3fz0"  sustained  by  ek.  Then  it  remains  to  be  seen 


88  BRIDGE  BUILDING. 

whether  gk  sustains  more  than  3§w/',  so  as  to  reduce 
the  horizontal  thrust  of  Ik  below  that  of  ij. 

"With  the  truss  fully  loaded  except  at  the  point/,  ij 
sustains  verticalljjlGi^,  whence^,  having  the  same  hori 
zontal  thrust  exerts  a  depressive  force=f  16w",=10f  w", 
atj,  leaving  a  balance  of  5Ji#",  exerted  by  ij  toward 
lifting  the  7w"  at  g.  Hence,  only  If  w"  remains  as  the 
weight  sustained  by  gk.  Therefore,  the  horizontal  pull 
of  e/c,  is  not  less  than  that  of^A;,  the  horizontal  thrust 
of  Ik,  is  not  less  than  that  of  ij ,  and  its  lifting  power, 
not  less  than  5 \w",  and  ek  does  not  lift  more  than  3f  w"y 
nor  as  much  as  when/  and  g  are  without  load,  as  de 
termined  by  the  process  above  explained. 

XXXI.  To  determine  the  greatest  stress  to  which 
dl  is  liable,  let  the  weights  at  e,/and  g  be  removed. 
Then  the  pressure  at  z,  due  to  the  weights  at  6,  c  and 
d,  equals  6w",  that  is,  Iw"  for  weight  at  6,  2w"  for  that 
at  Cj  and  3w"  for  that  at  d.  We  therefore  takejg"  on 
ij  produced,  to  represent  the  thrust  of  ?J,  produced  by 
610"—- draw  q"r"  parallel  with  fj,  and  from  q"r"  find /I" 
(of  course  less  than//'),  and  having  taken  kv'  on  jk 
produced,  equal  to  jr",  raise  the  perpendicular  vV  = 
ft",  and  draw  x'y'  parallel  with  ek.  Then,  x'y'  repre 
sents  the  tension  of  ek,  from'which  we  find  ea",  repre 
senting  the  vertical  thrust  of  el  at  its  maximum.  Also 
kyf  represents  the  thrust  of  kl\  and,  having  taken  Id' 
on  kl  produced,  equal  to  ky',  raise  the  vertical  d'e',  equal 
to  ea"  from  e',  draw  e'f,  parallel  with  dl,  and  meeting 
Im  (produced,  if  necessary),  in/,  and  e'f  represents  the 
tension  of  dL 

We  have  a  short  way  of  verifying  the  correctness  or 
otherwise  of  the  last  result,  since  we  know  that,  in  the 
state  of  the  load  here  assumed,  6w",  is  transferred  from 


SEVEN  PANEL  TRUSSES.  39 

the  left  to  the  right  of  the  centre,  necessarily  through 
the  tension  of  de,  the  only  member  capable  of  perform 
ing  that  office.  Hence  the  tension  of  dl  in  this  case, 
can  be  neither  more  nor  less  than  what  is  due  to  a  lift 
ing  power  equal  to  6w".  Then,  taking  dc'  on  dm,  to 
represent  610",  and  drawing  the  horizontal  c'b',  we  have 
do'  to  represent  the  tension  of  dl,  and,  if  e'f=*dbf,  the 
result  is  probably  correct.  We  know,  moreover,  that 
6*0"  is  the  greatest  weight  ever  transferred  past  the 
centre  of  the  trass,  the  left  hand  side  having  the  great 
est  possible  load,  and  the  right  hand  side,  the  least 
possible.  Therefore,  di'  represents  the  maximum 
stress  for  dl,  which  is  equal  to  §w"^tl*  +  v* 

V 

XXXII.  If  the  points  6  and  c  alone  be  loaded,  we 
know  that  8tf/'  is  transferred  through  dl,  and  there 
being  no  weight  at  d9  this  lifting  force  of  dl,  must  be 
sustained  by  the  thrust  of  dm.     Having  then,  found  If 
representing  thrust  of  ml,  by  a  process  similar  to  that 
by  which  we  obtained  //'in  the  preceding  case,  that  is, 
commencing  with  jq"f,  representing  the  thrust  of  ij 
under  a  weight  equal  to  3*0",  we  take  mg'  =•  If*  on  lin 
produced,  raise  the  vertical  g'i'  equal  to  a  line  repre 
senting  3w",  and  draw  i'i'  parallel  with  cm,  when  we 
have  i'f  to  represent  the  tension  of  cm. 

XXXIII.  Or,  we  may  take  ok'  on  ao  produced,  to  re 
present  the  thrust  of  ao,  due  to  the  vertical  pressure 
(=  Ht0")  at  a,  resulting  from  the  weights  at  6  and  c, — 
draw  the  vertical  k'l',  representing  lw",  =  weight  at  6, 
and  cutting  on  produced  in  mf,  and  I'm'  represents  the 
lifting  force  exerted  by  bn ;  as  is  made  obvious  by 
forming  the  parallelogram  I'n' ,  upon  the  diagonal  om'. 

* gf  i'  andy  shown  in  Diagram  B,  to  avoid  complication 


40  BRIDGE  BUILDING. 

Take  bo'  =  I'm' ,  and  draw  the  horizontal  o'//,  then  bp' 
represents  the  tension  of  bn,  and  ow7,  the  thrust  of  on. 
Take  nar=  om',  on  on  produced,  draw  a  b/  =  bp',  paral 
lel  with  bn,  and,  from  bn  let  fall  btct  representing  the 
weight  (  =7  w")  at  c,  and  the  part  below  nm,  represents 
the  lift  of  cm,  whence  we  derive  the  tension  of  cm. 
The  result  should  he  the  same  as  that  obtained  by  the 
former  operation. 

XXXIV.  If  the  point  b  only,  be  loaded,  we  may 
take  ok"  to  represents  the  thrust  of  ao  resulting  from  a 
pressure  of  6?0"  at  a,  let  fall  k"l"  cutting  on  in  m",  to 
represent  the  Iw"  at  6,  and  m"l"  represents  the  vertical 
lift  of  bn.     Make  bo"  =  m"i",  and  draw  the  horizontal 
o77/)77,  and  we  have  bp"  representing  the  tension  of  bn. 
This  is  the  maximum  stress  of  6?z,  since  6/?,  can  only 
sustain  the  weight  at  b,  less  the  excess  of  lifting  power 
of  ao  over  the  depressing  power  of  on,  both  having  the 
same  horizontal  thrust;  which  excess  is  represented 
by  k'm'  and  k"m",  and  is  least  when  the  weight  bearing 
at  a  is  least.     But  the  bearing  at  a  (and  the  lift  of  ao), 
can  never  be  less  than  f  of  the  weight  at  b,  and  k"m" 
etc.,  can  never  represent  less  than  f  weight  at  6,  or  J 
of  the  lift  of  ao;  whence  m"l"  etc.,  can  never  represent 
more  than  f  weight  at  b ;  consequently  bn  can  never 
sustain  a  weight  greater  than  5w"  which  is  the  amount 
represented  by  m"V  when  b  is  fully  loaded,  and  the  re 
mainder  of  the  truss  without  load. 

XXXV.  With  regard  to  cm,  no  simple  and  conclu 
sive  reason  presents  itself,  why  the  result  above  ob 
tained  for  the  stress  of  that  member  when  b  and  c  alone 
are   loaded,   is   the   actual   maximum.      But,   as   the 
assumed  condition  is  precisely  analogous,  as  far  as  the 


SEVEN  PANEL  TRUSSES.  41 

case  permits,  to  the  conditions  under  which  all  the 
other  diagonals  have  been  shown  to  suffer  their  maxi 
mum  stresses,  it  is  reasonable  to  conclude  from  analogy, 
and  the  general  nature  of  the  case,  that  wre  have  ob 
tained  the  true  maximum  stress  for  cm.  Should  there 
be  doubt  whether  some  supposable  distribution  of  load 
upon  the  truss,  would  not  produce  greater  stress  than 
that  above  shown  for  the  member  in  question,  it  is 
presumed  that  such  doubt  would  readily  be  set  aside 
by  an  analysis  similar  to  what  has  already  been  gone 
through  with. 

UPRIGHTS,  OR  VERTICAL  MEMBERS. 

XXXVI.  It  has  already  been  seen  [xxvm],  that  the 
maximum  tension  of  verticals  equal  w,  throughout. 
We  have  also  seen  [xxxiv],  that  the  lift  of  bn,  is  always 
less  than  the  weight  at  b ;  consequently  ob  is  never  ex 
posed  to  compression,  unless  the  load  be  applied  at  the 
arch,  which  will  seldom  be  found  advisable. 

When  cm  exerts  its  maximum  lift,  the  point  c  is 
loaded,  and  the  lifting  force  of  cm  is  all  expended  upon 
the  weight  at  c.  But  when  the  point  b  alone  is  loaded, 
cm  exerts  a  lift,  which  is  the  measure  of  the  maximum 
compression  of  en,  resulting  from  tension  of  cm,  since 
any  weight  at  the  right  hand  of  c,  would  bring  more 
or  less  downward  action  at  the  point  m,  thereby  reliev 
ing  some  of  the  tension  of  cm,  and  consequently, 
diminishing  its  compressive  action  upon  bn.  The  com 
pression  exerted  upon  en  by  the  tension  of  cm,  is  found 
to  be  about  equal  to  2w",  and  very  nearly  the  same  as 
that  exerted  by^)',  and  represented  on  the  diagram  by 
ft'  [xxix],  2w",  then,  may  be  regarded  as  the  maximum 
compression  of  en. 
6 


42  BRIDGE  BUILDING. 

The  vertical  dm,  can  never  suffer  compression  to  ex 
ceed  3  w",  =  greatest  weight  sustained  by  dl  when  d  is 
without  load ;  and  if  d  be  loaded,  so  as  to  add  to  the 
lift  of  dl,  any  weight  at  d,  relieves  dm  of  4  pounds  of 
compression,  to  every  three  pounds  added  to  the  lift 
of  dl,  so  that  lw"  at  d,  while  it  increases  the  lift  of  dl 
from  Sw "  to  6w",  changes  the  action  of  dm,  from  com 
pression  of  3w",  to  tension  of  ~Lw". 

XXXVII.  Having  determined  the  maximum  weights 
sustained  by  the  several  diagonals  and  verticals,  we 
proceed  to  ascertain  their  respective  stresses,  and  re 
quired  amounts  of  material ;  as  depending  upon  the 
length  of  each  member,  multiplied  by  its  maximum 
stress. 

The  greatest  weight  sustained  byjf)',  as  measured  on 
the  diagram,  and  verified  by  calculation,  is  equal  to 
810",  or  f  w ;  and  the  length  being  equal  to  \X/i2-f-ji;2,  the 
stress  equals  f  x/A'J-Hp3  w,  and  the  required  material 

V 

equals  (- —  +  23g  V)M.  The  4  diagonals  gk,  ek,  bn  and  nd, 
sustain,  each,  a  maximum  weight  of  5w",  [xxxiv],  with 

length  =  v'/r+le^'     Hence,  stress  equ als  |%/AM-  lf-«aw, 

10 

and,  material  for  each,  =  (^+  \\ f  V)M. 

The  four  remaining  diagonals  sustain  each  a  maxi 
mum  weight  of  6w",  =  f  w,  with  length  =  >//^  _j_  v*9 
giving  stress  equal  to  j y/Aa  +  <&  w,  whence  material 

10 

equals  (5^!  -f  $v)  M.  Then,  multiplying  the  last  two 
coefficients  of  M  by  four,  and  the  preceding  one  by  two 
for  the  number  of  pieces  in  each  class ;  adding  the 
products,  and  annexing  the  common  factor  M,  we 


SEVEN  PANEL  TRUSSES.  43 

obtain  for  the  ten  diagonals,  an  amount  of  material 
equal  to  (7.14^+5.6260)M. 

The  aggregate  length  of  verticals,  equals  4-|  y,  and 
their  greatest  tension  stress  equals  w.  Hence,  4.666#,M 
represents  the  amount  of  tension  material  they  re 
quire. 

The  two  longest  verticals  sustain  a  maximum  com 
pression  of  3tf?"  [xxxvi],  or  %w,  with  length  =-  v. 
Hence  material  =  0.857vM.  The  two  next  in  length 

O 

sustain  compression  =  |tt;,  with  aggregate  length  =  l§i?, 
and  require  compression  material  =  0.476t>M,  mak 
ing  the  whole  amount  of  required  material,  as  repre 
sented  by  the  amount  of  action  by  compression  on 
verticals=  1.333M. 

We  have,  then,  material  for  the  whole  truss,  as  re 
presented  by  the  amount  of  action,  as  follows  : 

Under  Compression. 
Arch,  [xxvn] 
Verticals, 


Total,  .............................................  (42-  +  6u)M 

Under  Tension. 
Chord,  [xxvn]  ...........................  (42^  ..............  M) 

Diagonals,  .........................  .  .......  (7.14^  -f  5.626v)M 

Verticals,  ...................................      _  4.666?;M 

Total,  .....................  ................  49.14|'-f  10.292^M 

Making  h  =»  v  •»  1,  these  amounts  become  : 
Under  Compression,  48M.     Under  Tension,  59.432M.* 

*  The  difference  between  this  result,  and  that  given  in  the  synopsis 
on  page  20  of  my  original  work,  arises  from  the  fact  that  one  was 
based  on  a  circular  arch,  and  the  stresses  takuu  from  the  diagram,  and 


44  BRIDGE  BUILDING. 

XXXTII.  The  preceding  results  are  based  on  the 
assumption  [xxvn]  that  the  maximum  tension  of  the 
chord,  and  the  maximum  horizontal  thrust  of  the  arch 
in  all  parts,  are  equal  to  the  horizontal  thrust  of  the 
end  sections  of  the  arch  when  the  truss  is  fully  and 
uniformly  loaded.  Although  this  may  seem  self- 
evident,  it  may  not  be  amiss  to  make  particular  men 
tion  of  some  of  the  conditions  affecting  the  case,  which 
may  lead  to  a  better  understanding  of  the  subject,  if  it 
fails  to  amount  to  an  absolute  demonstration. 

The  arch  and  chord  obviously  act  and  react  upon  one 
another  horizontally  from  end  to  end,  and,  as  weight 
removed  from  any  part  of  the  length,  diminishes  the 
amount  of  bearing  at  both  ends,  which  bearing  go 
verns  the  stress  at  the  ends,  it  follows  that  the  ends,  at 
least,  of  both  arch  and  chord,  have  their  greatest  stresses 
under  a  full  load  of  the  truss. 

It  is  obvious,  also,  that  no  part  of  arch  or  chord  can 
have  greater  stress  than  the  ends,  unless  it  be  commu 
nicated  by  the  tension  of  diagonals.  When  the  acting 
diagonals  all  incline  one  way,  their  united  horizontal 
action  only  equals  the  difference  between  the  horizon 
tal  thrust  of  the  two  end  sections  of  the  arch,  and  the 
action  of  chord  and  arch  can  no  where  be  greater  than 
at  the  end  from  which  the  acting  diagonals  incline. 

When  acting  diagonals  incline  inward  from  the  ends, 
the  intermediate  portions  of  chord  and  arch  are  under 
less  stress  than  the  end  portions,  and  consequently, 
less  than  they  sustain  under  a  full  load  of  the  truss. 
But  when  acting  diagonals  incline  outward,  toward  the 

the  other,  on  a  parabolic  arch,  and  stresses  mostly  calculated  numeri 
cally  ;  and,  from  the  further  fact  that  in  one  case,  the  weight  was  as 
sumed  to  be  applied  at  the  arch,  and  in  the  other,  at  the  chord  ;  the 
former  producing  more  compression,  and  the  latter,  more  tension  upon 
the  uprights. 


SEVEN  PANEL  TRUSSES.  45 

ends  of  the  truss,  the  intermediate  portions  of  arch  and 
chord  are  under  horizontal  stress  greater  than  that  of 
the  end  portions,  by  an  amount  equal  to  the  aggregate 
horizontal  action  of  all  the  acting  diagonals  inclining 
toward  the  respective  ends. 

Now,  as  no  more  than  two  diagonals  inclining  toward 
the  end  bearing  the  greatest  weight,  can  be  in  action 
at  the  same  time,  in  a  seven  panel  truss,  the  question  re 
solves  itself  into  —  whether  two  diagonals  acting  in  one 
direction,  can  ever  exert  force  enough  to  over  balance 
the  loss  of  action  of  the  end  section,  resulting  from  di 
minished  bearing  at  the  abutment,  consequent  upon 
the  removal  of  load,  on  which  removal,  the  action  of 
diagonals  depends  ? 

As  to  that  question,  the  removal  of  weight  from  the 
central  portion  of  the  truss,  must  bring  into  action  in 
wardly  inclined  diagonals,  while  removing  weight  from 
one  end  only,  can  bring  into  action  no  diagonals  in 
clined  toward  the  full  loaded  end,  whence  the  weight 
bearing  at  that  end  indicates  the  greatest  stress  of  any 
part  of  chord  and  arch  which,  of  course,  is  less  than 
under  the  full  load  of  the  truss. 

There  remains  then,  only  the  case  of  removal  of  load 
from  both  ends  of  the  truss,  which  can  produce  any 
considerable  action  upon  diagonals  inclined  outward, 
so  as  to  give  greater  stress  to  the  middle,  than  the  end 
portions  of  the  arch  and  chord.  If  the  weights  at  6 
and  g  be  removed,  the  pressure  at  each  abutment  is 
diminished  by  J  of  the  maximum,  or,  by  7i0";  and  jf;, 
sustaining  only  Bwff  at  the  maximum,  and  having  the 
same  inclination  as  ij9  its  horizontal  action  could  only 
balance  the  effect  of  %w"  removed  from  ij  ;  while  ek, 
even  if  it  sustained  its  greatest  weight  of  5?0",  as  it 
evidently  does  not,  in  this  case,  would  only  exert  the 


46  BRIDGE  BUILDING. 

same  horizontal  action  as  ij  would  do  under  8*0". 
Hence  these  two  diagonals,  under  their  maximum 
stresses,  which  neither  suffers,  in  the  present  case, 
would  only  compensate  f  of  the  loss  on  stress,  of  arch 
and  chord,  due  to  removal  of  weight  from  the  truss. 

It  may,  therefore,  he  regarded  as  a  matter  of  extreme 
probability,  if  not  a  rigidly  demonstrated  fact,  that  the 
arch  and  chord  of  an  arch  truss,  undergo  their  maxi 
mum  stress  in  all  parts,  under  the  full  uniform  load  of 
the  truss. 

It  is  hoped  and  believed  that  the  foregoing  illustra 
tious  of  the  manner  of  determining  the  strains  of.  the 
several  parts  and  members  of  an  arch  truss  of  seven 
panels,  will  be  sufficient  to  enable  the  same  to  be  done 
in  the  case  of  trusses  of  any  desired  number  of  panels. 


THE  TRAPEZOIDAL  TRUSS. 

So  designated  from  the  figure  of  its  outline. 

XXXIX.  This  truss  may  be  constructed  with  dia 
gonals  and  verticals,  as  in  Fig.  12,  or  without  verticals, 
except  at  b  and  #,  as  seen  in  Fig.  13.  To  explain  the 
operation  of  these  trusses,  and  determine  the  maximum, 
stresses  of  their  various  parts,  we  may  use  the  same  no 
tation,  generally,  as  heretofore  ;  that  is,  let  h  represent 
the  horizontal,  and  v,  the  vertical  reach  of  the  diagonal 
or  oblique  members,  and  D,  the  length  of  diagonals. 
Also,  let  w  represent  the  greatest  movable  load  for  a 
panel  length,  supposed  to  be  concentrated  at  the  nodes 
6,  <?,  d  etc.,  of  the  lower  chord  ;  and,  let  w"  be  equal 
to  w,  divided  by  the  number  of  panels  in  the  truss  (7, 
in  this  case),  i.e.,  let  w  =  lw". 

Then,  supposing  the  diagonals  (Fig.  12),  not  includ 
ing  the  king  braces,  ao  and  ij  at  the  ends  ;  the  verticals 


TRAPEZOIDAL  TRUSS. 


47 


ob  andjgr,  and  the  lower  chord,  to  act  by  tension  ;  and 
the  upper  chord,  or  boom,  the  king  braces,  and  the 
four  intermediate  verticals,  to  act  by  thrust,  or  com 
pression  —  if  a  weight  (w)  be  applied  at  6,  it  will  ob 
viously  cause  a  downward  action  equal  to  w"  at  i9  and 
one  equal  to  6w"  at  a. 

FIG.  12. 
1  23 


ra 


4 
10 
I 


5 

15 
k 


6 

21 

j 


a  b  c  d          e          f          g  i 

Now,  from  what  has  already  been  seen,  in  the  discus 
sion  in  relation  to  Fig.  10,  the  weight  acting  at  i,  can 
only  do  so  by  acting  successively,  or  simultaneously, 
upon  6tt,  and  each  diagonal  parallel  with  bn  on  the  right, 
by  tension,  and  upon  each  compression  upright  and 
the  king  brace  ?)',  by  thrust ;  causing  upon  each  of 
these  10  members,  a  stress  equal  to  w"  upon  verticals, 
and  equal  to  w"—  upon  obliques ;  D  representing  the 
length  of  obliques,  or  diagonals. 

A  weight  (w)  at  c,  in  like  manner,  causes  a  pressure 
of  2w"  at  i,  through  cm,  and  other  diagonals  inclining 
to  the  right,  on  the  right  hand  of  c.  Also,  a  pressure 
of  610"  at  a.  But  co  being  the  only  member  that  can 
transfer  weight  from  c  to  the  left,  and,  co  and  bn  be 
ing  antagonistic  — stress  upon  the  one  tending  to  relax 
the  other,  the  result  must  be,  that  both  can  not  act  at 
the  same  time,  from  the  effects  of  weight  at  b  and  c, 
and  only  that  one  can  act,  to  which  the  greater  weight 
is  applied ;  and  that,  only  with  the  excess  of  weight 
acting  upon  it,  over  what  is  acting,  or  tending  to  act 
upon  the  other.  Now,  as  the  load  at  c,  tends  to  throw 


48  BRIDGE  BUILDING. 

a  weight  of  5w"  upon  co,  while  the  load  at  b  tends  to 
throw  It0"  on  bn,  the  former  tendency  must  prepon 
derate  —  c.o  must  sustain  4*0",  while  bti  is  relaxed,  and 
the  whole  weight  at  6,  is  sustained  by  the  tension  of  oh. 
In  reality  then,  cm  sustains  f  of  the  weight  at  c,  and 
none  of  that  at  b. 

Still,  the  result  is  the  same,  as  to  pressure  at  a  and 
i,  the  former  point  supporting  lw"  ,=  the  whole  of  the 
load  at  6,  plus  4?0"  of  that  at  <.',  making  11 10",  =  pres 
sure  due  at  a,  from  the  weights  at  6  and  e,  while  the 
point  i  supports  oio",  all  out  of  the  weight  ate.  Thus, 
cm,  dl  etc.,  sustain  the  same  proportion  of  the  aggre 
gate  weights  at  6  and  c,  as  if  each  weight  acted  sepa 
rately,  and  independently  of  the  other. 

Again,  applying  a  weight  (w\  at  rf,  8i0"  tends  to  bear 
at  i,  and  4?0"  at  a,  through  dn  and  co.  But  as  we  have 
3*0"  tending  to  act  on  CM,  as  already  seen,  this  is  neu 
tralized  by  the  tendency  to  action  upon  rfw,  and  only  a 
surplus  of  1*0",  really  acts  upon  dn  in  this  case,  while 
the  610",  =  pressure  due  at  £,  from  the  weights  at  6,  c 
and  </,  is  all  made  up  out  of  the  single  weight  at  d, 
and  the  whole  of  the  weights  at  6  and  c,  together  with 
IMJ"  from  that  at  </,  comes  to  bear  at  «,  giving  a  pressure 
of  15?r",  at  that  point ;  still  the  same  as  if  each  weight 
acted  independently  of  the'  others.  And,  in  general, 
each  diagonal,  at  all  times,  sustains  the  preponderance 
of  weight  tending  to  act  upon  it,  over  that  which  tends 
to  act  at  the  same  time  upon  its  antagonist.  Hence 
the  greatest  weight  sustained  by  any  diagonal,  is  when 
all  the  weight  tending  to  act  upon  it,  is  upon  the  truss, 
and  none  of  the  weight  tending  to  produce  action  upon 
its  antagonist,  or  counter. 

Thus,  when  6  alone  is  loaded,  \ic"  is  sustained  by  bn, 
but  when  any  point  on  the  right  of  6  is  loaded,  there  is 


TRAPEZOIDAL  TRUSS.  49 

tendency  to  action  by  co,  and  the  action  of  bn  is  de 
stroyed  or  diminished.  Therefore  \w"  is  the  maximum 
weight  sustained  by  bn.  When  b  and  c  alone  are 
loaded  with  the  weight  (w)  at  each,  cm  sustains  810", 
as  already  seen,  with  no  tendency  to  action  in  dn. 
But  if  <-/,  or  any  point  on  the  right  of  c,  be  loaded,  there 
is  tendency  to  action  in  dn^  which  must  diminish  or 
destroy  the  action  of  cm.  Hence,  cm  sustain*  its  max 
imum  weight  (=  3tf/'),  when  the  points  6  and  c  alone 
are  under  their  full  load.  And,  it  must  be  obvious 
that  the  maximum  weight  is  sustained  by  each  d&gonai 
inclining  to  the  right,  when  the  point  at  its  lower  end, 
and  all  the  nodes  at  the  left  are  fully  loaded,  and  all 
those  at  the  right  are  without  load.  Hence  we  esta 
blish  the  following  easy  and  expeditious  practical  method 
of  determining  the  maximum  weights  and  stresses- 
upon  this  class  of  members,  in  trusses  with  any  number 
of  panels. 

XL.  Having  made  a  rough  diagram  of  the  truss,  as 
Fig.  12,  for  instance,  place  over  the  nodes  o,  n,  ra,  &c., 
the  numbers  1,  2,  3,  &c.,  high  enough  to  admit  of  a  sec 
ond  series  under  the  first,  formed  by  repeating  the  1 
under  itself,  adding  the  1  and  2  together  and  placing  the 
sum  (3),  under  the  2  in  the  upper  series..  Then  add  1, 
2  and  3,  and  place  the  sum  (6)  under  3,  and  so  on,  plac 
ing  under  each  figure  of  the  upper  series,  the  sum  of 
that  figure,  and  all  those  at  the  left,  in  said  upper  series. 

Then,  it  will  be  seen  that  each  figure  in  the  upper 
line,  prefixed  to  w",  shows  the  pressure  caused  at  the 
right  hand  abutment,  by  the  weight  (w)  directly  under 
the  figure,  e.  g.,  the  upper  figure  3  over  d,  indicates 
that  %w"  is  the  bearing  at  i,  produced  by  the  weight 
(w)  at  d,  and  so  of  the  other  figures  in  the  upper  line. 
7 


60  BRIDGE  BUILDING. 

In  the  mean  time,  the  figures  in  the  lower  line,  show 
the  accumulation  of  the  effects  of  the  different  weights 

O 

upon  successive  diagonals  from  left  to  right.  Thus, 
the  figure  6  over  the  point  d,  shows  that  dl  sustains 
6w",  =  pressure  due  at  z,  from  weights  (w)  at  b,  c  and 
d,  when  those  points  only  are  loaded  ;  in  which  case, 
dl  sustains  its  maximum  weight,  as  before  seen. 

In  like  manner,  the  figures  10  &  15  over  eand  /,  indi 
cate  that  10w"  and  15w",  are  respectively  the  maxi 
mum  weights  sustained  by  ek  and  fg,  while  2lw"  (  = 
3w),  equals  the  maximum  weight  sustained  by  ?J,  (by 
compression,  of  course),  when  the  whole  truss  is  loaded. 

XLI.  Having  thus  ascertained  the  greatest  weights  the 
several  oblique  members  are  liable  to  sustain  (those 
inclining  to  the  left  being  obviously  exposed  to  the 
same  stresses  as  those  inclining  to  the  right),  we  find 
their  maximum  stresses  by  rule  4,  [xvi];  i.  e.,  multiply 
the  weight  by  the  length,  and  divide  by  the  vertical 
reach  of  the  member.  Thus,  the  maximum  compres 
sion  of  ?J,  equals  3w-,  =  SM;  \//<  •+  r,  and  the  repre- 

v 

eentative  of.  required  material,   is  (—  -f-  3f)  M. 

The    maximum    stress    of    ek     equals    10^"-  = 
Ifw  v^'  +  '^  and   its   representative   for  material    is 

V 

(1 3^!  4.  l|«f)jf.  Or,  the  lengths  and  inclinations  being 
the  same,  we  may  take  the  aggregate  maximum  weights 
sustained  by  tension  diagonals,  reduced  to  terms  of  ?/;, 
multiply  by  the  square  of  the  common  length,  divide 
by  v,  and  change  w  to  M.  The  ten  tension  diagonals 
sustain  maximum  weights  equal  to  w"  multiplied  by 
twice  the  sum  of  all  the  figures  in  the  lower  line  over 


TRAPEZOIDAL  TRUSS.  51 

the  diagram,  except  the  last,  making  70w",=10i0,  and 
require  material  =  (lO-  +  lOi?)  M. 

The  tension  verticals  06  and  jg,  sustain  the  weights  (w) 
acting  at  b  aud#  when  the  truss  is  fully  loaded,  which  is 
their  maximum  stress,  and  they  require  material  for 
the  two,  =  2nn. 

The  thrust  uprights  el  and  //:,  receive  and  sustain 
the  maximum  sustained  by  dl  and  ek  respectively, 
which  are  the  measures  of  their  respective  stresses  of 
compression,  being  §w"  for  el,  and  10w"  for  /fc,  and 
the  same  for  dm  and  eft,  making  an  aggregate  weight 
of  4$w,  whence,  their  representative  for  material  is 


XLII.  With  regard  to  stress  of  the  lower  chord,  the 
tension  of  ac  equals  the  horizontal  thrust  of  «o,  and  of 
course  is  greatest  when  ao  sustains  the  greatest  weight  ; 
which  is  manifestly  under  the  full  load  of  the  truss.  The 
tension  of  cd  equals  the  horizontal  thrust  of  ao  (through 
flc),  and  the  horizontal  pull  of  oc  ;  and  must  be  greatest 
when  the  combined  action  of  ao  and  oc  is  greatest.  Now, 
although  the  weight  borne  by  oc  is  greater  by  w"  when 
the  point  b  is  unloaded,  than  under  the  full  load,  on 
the  other  hand,  the  weight  on  ao  is  less  by  6w",  so  that 
the  combined  action  of  the  two  members,  must  be 
greatest  when  the  truss  is  fully  loaded;  since  no  other 
change  can  increase  the  action  of  either. 

Again,  de  sustains  the  horizontal  action  of  ao,  oc  and 
nd,  when  the  truss  is  under  a  full  load  ;  dl  and  em  being 
inactive  in  that  case,  since  the  tendency  to  action  is  the 
same  in  each,  whence  neither  can  act.  Therefore  nd 
sustains  simply  the  weight  (w)  at  d\  oc  sustains  the 
two  weights  at  c  and  a1,  =  2t0,  while  ao  sustains  the 
same,  with  the  addition  of  the  weight  at  6,  making  6w 


52  BRIDGE  BUILDING. 

sustained  by  the  three  members  contributing  to  the 
tension  of  de.  Now  while  the  maximum  weights  sus 
tained  by  oc  and  nd,  exceed  by  only  4w/'  what  they 
sustain  under  a  full  load,  neither  can  be  brought  under 
its  maximum  stress,  without  removal  of  load  from  6 
in  one  case,  and  from  both  b  and  c  in  the  other,  thereby 
diminishing  the  weight  on  ao,  by  6w"  in  one  case,  and 
by  llw"  in  the  other.  Hence  the  stress  of  de  is  greatest 
under  a  full  load  of  the  truss,  and  as  already  seen, 
equals  the  horizontal  action  of  weight  equal  to  6w  upon 
oblique  members  of  vertical  reach  equal  to  v,  and  hori 
zontal  reach  equal  to  h.  The  maximum  stress  of  de, 
then,  equals  6t0-,  and  that  of  cd  equals  the  same,  less 
the  horizontal  pull  of  dn,  due  to  the  weight  (20)  at  d, 
and  is  therefore  equal  to  5tt*-. 

"We  have  for  the  lower  chord,  then,  one  section,  de 
(with  length  equal  to  h),  exposed  to  stress =  Qw— 

Two  sections,  cd  and  cf,  with  stress =  610— ^ 

Four      do.,     ac  and^, =  810- ; 

whence,  adding,  multiplying  by  h,  and  changing  w  to 
M,  we  have  to  represent  required  material,  28— M. 

XLIII.  It  is  scarcely  necessary  to  state  that  the  ob 
lique  members  ao,  and  oc,  exert  at  o  in  the  direction 
from  o  to  n,  the  same  force  that  they  exert  in  the  oppo 
site  direction  upon  cd.  In  fact,  the  thrust  of  on,  and 
the  tension  of  cd,  simply  act  and  react  upon  one  ano 
ther  through  the  media  of  ao,  oc  and  ac,  whence  the 
compression  of  on,  must  be  just  equal  to  the  tension  of 
cd;  and  furthermore,  the  thrust  of  nm  is  the  indirect 
counteraction  of  the  tension  of  de;  and,  as  the  two 
forces  are  in  opposite  and  parallel  directions,  they  must 
be  equal,  being  in  equilibrio.  Also,  mlk  must  sustain 


TRAPEZOIDAL  TRUSS.  53 

the  same  compression  as  ww,  throughout,  since  the 
diagonals  meeting  the  chord  at  m  and  /,  are  inactive 
under  the  fall  load  of  the  truss.  Of  course,  kj  is  liable 
to  the  same  maximum  action  as  on. 

From  what  precedes,  it  cannot  fail  to  be  obvious 
that  the  maximum  action  of  all  parts  of  the  upper  chord 
occurs  at  the  same  time  with  that  of  the  lower  chord, 
namely,  under  the  full  load  of  the  truss.  We  have 
then,  two  sections  liable  to  a  compression  of  5^.,  and 

three,  liable  to  6w-;    whence   the    representative   of 

required  material,  is  28— M.  We  may  now  sum  up 
the  material  for  the  truss,  required  to  support  the  as 
sumed  movable  load  through  all  the  changes  liable  to 
take  place,  as  follows  : 

Material  under  Compression. 
Chord, (28^  XM 

King  Braces,  [XLI] 

Posts,  [XLI] 

Total, (34-£  +  10|v)M 

Under  Tension. 
Chord,[xLii] (28-*-  x  M 


Diagonals,  [XLI] (10 

Verticals,  [XLI] 2m 


Total, , (38     +  12i?)M 

Making  h  —  v  =»  1,  we  have : 

Compression  material, 

Tension  material,  =  50M 

For  Arch  Truss,  Comp.  Mat.,  [xxvn] =  48M 

"          "      Tension  do.,  =  59n 


54  BRIDGE  BUILDING. 

XLIY.  A  trapezoidal  truss  without  verticals  (ex 
cept  at  one  panel  width  from  the  ends),  is  represented 
in  Fig.  13.  The  members  ob  and  oc,  as  alsoj*/  and  fj, 
are  supposed  to  be  so  formed  and  connected  as  to  act 
by  tension  only,  and  the  other  diagonals,  so  as  to  be 
capable  of  acting  either  by  thrust  or  tension. 


FIG.  13. 


If  a  weight  (?(?),  be  applied  at  6,  it  will  cause  a  bear 
ing  of  \w"  at  i,  and  §w"  at  a,  the  same  as  in  the  case 
of  Fig.  12.  Now,  this  weight  at  6,  might  (if  bn  were 
removed,  and  oc  were  capable  of  withstanding  com 
pression),  be  suspended  entirely  by  06,  and  supported 
by  ao  and  oc,  in  proportion  to  the  bearing  produced 
by  it  at  a  and  i  respectively.  But  as  bn  is  able  to  act 
by  tension,  and  oc  unable  to  act  by  thrust,  the  6w" 
bearing  at  a,  acts  through  bo  and  oa,  while  the  IM/' 
bearing  at  i,  must  first  act  by  tension  upon  bn  ;  secondly, 
by  thrust  upon  nd,  since  that  is  the  only  member  meet 
ing  bn  at  7?,  capable  of  sustaining  weight.  Hence,  the 
action  of  the  weight  is  transferred  to  d,  and  through 
dl  to  I,  thence  to/,  and  so  on  through  fj,  andjV,  to  the 
abutment  at  £;  acting  alternately  by  tension  and 
thrust,  upon  six  oblique  members,  producing  the 
same  amount  of  action  (=  w"-\  upon  each. 


TRAPEZOIDAL  TRUSS.  55 

Another  weight  (w)  at  c,  must  cause  pressure  at  z, 
equal  to  2w" ',  and  at  a,  equal  to  5w".  The  action  there 
fore,  must  be  divided  between  cm  and  oc,  in  the  pro 
portion  of  2  to  5,  producing  alternately  tension  and 
thrust,  through  the  points  w,  e,  k,  gj  to  i ;  on  the  right, 
and  through  co  and  oa,  to  a,  on  the  left. 

Thus  far,  the  weights  have  acted  upon  independent 
systems  of  oblique  members  (except  as  to  king  braces), 
neither  weight  acting  upon  any  member  acted  on  by 
the  other.  But  when  a  weight  (w)  is  imposed  at  d,  it 
must  act  upon  the  same  members  acted  on  by  the 
weight  at  b.  The  3w"  to  be  transferred  to  z,  must  act 
by  tension  upon  dl,  in  concert  with  the  1/0"  of  the 
weight  at  6.  But  the  pressure  at  a,  must  be  increased 
by  4w/',  which  can  be  transferred  from  </,  only  through 
tension  of  dn,  and  dn  being  previously  occupied  in 
carrying  \w"  from  6,  by  compression,  it  follows,  since 
the  same  member  can  not  be  under  compression  and 
extension  at  the  same  time,  that  the  greater  force  must 
preponderate,  dn  being  brought  under  tension  clue  to 
the  difference  of  4 10"  tending  to  act  by  tension,  and 
lw"9  tending  to  act  by  thrust,  the  action  of  dn,  being 
changed  from  thrust  under  Iz0",  to  tension  under  3w". 
All  the  weight  at  6,  then,  is  sustained  by  60,  together 
with  Zw"  from  weight  at  d,  making  lOw",  which,  with 
bw"  from  weight  at  c,  makes  15w"  =  pressure  due  at  «, 
from  weights  at  6,  c  and  d. 

In  the  mean  time,  the  weight  at  d,  having  obstructed 
the  passage  of  \w"  from  b  to  the  right  hand  abutment, 
has  been  obliged  to  make  compensation,  by  sending 
4w"  of  its  own  gravitating  force,  nstead  of  3w"  owed 
by  it  to  the  bearing  at  i. 

Similar  changes  of  action  take  place  when  another 
weight  (w)  is  applied  at  e ;  which  tends  to  throw  3w" 


66  BRIDGE  BUILDING. 

by  tension  upon  em,  while  the  weight  ate  tends  to  throw 
2i0"  upon  it  by  thrust,  as  seen  above.  The  result  is, 
that  em  sustains  \w"  by  tension,  and  cm,  \w"  by  thrust, 
while  co  sustains  the  whole  weight  at  c,  in  addition  to 
lw"  from  e. 

Again,  a  weight  (iv)  at  /,  tends  to  throw  2w"  upon 
fl,  to  act  by  tension  ;  but  as//  is  already  occupied  by 
4w"  acting  by  thrust,  /  is  obliged  to  depend  entirely 
upon//;  at  the  same  time  turning  back  2w",  and  re 
ducing  the  weight  previously  on  If,  by  that  amount,  or, 
to  2w>". 

In  like  manner,  a  weight  applied  at  g,  finds  gk  sus 
taining  Qw"  by  thrust,  whereby  it  is  prevented  from 
pending  \wff  (due  from  it  at  a),  to  the  left,  through 
tension  afgk.  Hence,  the  whole  weight  at  ^ris  sustained 
by  jg,  and  the  weight  acting  on  kg  is  reduced  to  610". 

XLV.  Thus  we  see  that  each  diagonal  (except  oc  and 
fj,  excluded  by  hypothesis),  is  liable  to  compression 
from  weights  at  certain  points,  and  tension  from 
weights  at  other  points ;  and,  it  is  manifest  that  the 
greater  stress  of  either  kind,  on  each  diagonal,  is  when 
all  the  weights  are  on  the  truss,  which  tend  to  produce 
upon  it  one  kind  of  stress,  and  none  of  those  which 
tend  to  produce  the  opposite  stress. 

Hence,  if  we  place  the  numbers  1,  2,  3,  &c.,  over  the 
diagram,  as  in  case  of  Fig.  12.  [xxxix],  it  is  clear  that 
only  alternate  weights  act  upon  the  same  system  of 
diagonals;  that  only  weights  under  the  odd  numbers 
1,  3  and  5  act  upon  diagonals  meeting  the  lower  chord 
at  points  under  those  numbers;  and  so  of  the  weights 
under  the  even  numbers  2,  4  and  6.  We  therefore 
form  a  second  series  of  figures  under  the  first,  by  placing 
under  each  odd  number,  the  sum  of  that  number  and 


TRAPEZOID  WITHOUT  VERTICALS.  57 

all  the  preceding  odd  numbers,  and  under  eacli  even 
number,  the  sum  of  that  and  all  preceding  even  num 
bers.  Then,  the  number  in  the  second  line,  is  the  co 
efficient  ofwf/,  to  express  the  maximum  weight  acting 
by  tension  upon  the  diagonal  inclining  to  the  right, 
from  the  point  under  that  number,  and  by  thrust,  upon 
the  diagonal  meeting  the  former  at  the  upper  chord. 

For  instance,  the  figure  4  in  the  second  line,  over  d, 
shows  that  dl  and  If,  sustains  4i0",  the  former  by  ten- 
gion,  and  the  latter  by  thrust.  This  is  the  weight 
which  must  bear  at  z,  in  consequence  of  the  weights 
at  6  and  d,  the  only  weights  that  can  produce  those 
specific  actions  upon  those  members.  On  the  contrary, 
this  action  upon  dl  and  If,  is  only  liable  to  diminution 
from  weight  at  /,  which  tends  to  throw  2w"  upon  the 
left  abutment  through  tension  of  ft  and  thrust  of  dl9 
and  consequently  diminishes  the  action  upon  those 
members,  due  to  weights  at  b  and  d.  Therefore,  4w" 
is  the  greatest  weight  sustained  by  dl  and  If,  and  2?0", 
the  weight  sustained  by  them  when  the  points  b,  d,  and 
/are  loaded,  whether  the  other  nodes  are  loaded  or 
not.  There  is,  however,  an  alternative  in  this  case, 
which  will  be  noticed  hereafter. 

The  figure  1  over  6,  indicates  that  bn  sustains  \w" 
by  tension,  and  nd  the  same  by  thrust,  which  action  is 
reversed  by  weights  at  d  and  /,  which  tend  to  throw 
6*0"  upon  these  members,  namely,  4*0",  from  d,  and 
2w"  from/.  Hence,  bn  is  liable  to  \w"  by  tension,  and 
610"  by  thrust,  the  latter,  when  d  and  /  are  loaded, 
and  b  unloaded ;  and  to  5wf/  (acting  by  thrust),  when 
all  the  three  points  are  loaded. 

Then,  if  we  form  a  third  series  of  numbers  under 
the  second,  by  reversing  the  order  of  the  second,  the 
one  series  shows  the  tension,  and  the  other  the  thrust 
8 


58 


BRIDGE  BUILDING. 


to  which  a  member  is  liable.  But  as  thrust  action  is 
not  received  by  any  diagonal  directly  from  the  weight 
producing  it,  but  from  a  tension  diagonal  meeting  it  at 
the  upper  chord,  we  do  not  learn  the  thrust  of  a  dia 
gonal  from  the  figure  over  it,  at  either  end,  but  from 
the  figure  over  the  foot  of  the  diagonal  by  which  the 
compression  is  communicated. 

Having  arranged  the  diagram  as  above  explained, 
we  form  from  it  a  table  of  greatest  weights  sustained  by 
the  several  diagonals,  and  stresses  produced  thereby, 
both  of  tension  and  thrust,  remembering  that  tension 
weights  are  shown  by  one  series  of  figures  and  thrust 
weights,  by  the  reversed  series. 


Diagonals. 

Compression. 

Weights.      Stresses. 

Tension. 

Weights.  Stresses. 

Under  full  load. 

Weights. 
THK.                 TEN. 

bn  and  kg, 

Qw" 

j) 

ow/   ~~ 

7) 

Iw"    Iw"- 

V 

SM;" 

cm  and  If, 
dl  and  me, 

4  a 

2  " 

4u>"? 

V 

T} 
7) 

2"    2«>"? 

fl 

T-V 

4  "     4w/'- 

« 

2u?" 

ek  and  dn, 

1« 

y\ 

»• 

6  "    6w"- 

5  " 

fj  and  co, 

0 

9  "     9w"? 

0 

9  « 

13 

22 

Adding  and  doubling  the  several  weights,  we  deduce 
the  representatives  of  material. 
Under  Compression, (3|-  -f  3f.r)M 

Under  Tension, (6f-**  +  6fr)M 

The  2  verticals  sustain  each  I2w",  giving  3|i?M 

The  king  braces  ao  and  ij,  sustairl  3w?  each, 

requiring   material   for   the   two  =  (6—  4-  6i'jM 

XLYL  The  stress  of  chords  is,  as  in  case  of  Fig.  12, 
due  to  action  of  obliques,  and  may  be  fairly  assumed 


TRAPEZOID  WITHOUT  VERTICALS.  59 

to  be  greatest  under  a  full  uniform  load  of  the  truss. 
The  brace  ao  has  a  horizontal  thrust  =  21V'-,  =  ten 
sion  of  ab.  The  thrust  of  bn  (under  the  full  load),  adds 
bw"-  at  6,  making  26^"-  =  tension  of  be.  This  is  in- 

V  V 

creased  by  9i0"— for  tension  of  oc,  and  by  Zw"~  for 
thrust  of  cm,  making  S7w"—  for  tension  ofcd;  and,  add 
ing  5w"—  for  tension  of  dn,  and  subtracting  2w"—  for 
tension  of  dl  in  the  opposite  direction,  we  have  40z0  — 
=  tension  of  de. 

We  have  then,  1  section  sustaining  40M?"-=40w"- 
2      "  "          37  "       74   " 

2      "  "          26  "       52   " 

2      "  "  21  "       42   " 

Making  a  total  stress=208i0"— =29f  10— actingupon sec 
tions  of  a  common  length  equal  to  A,  and  therefore, 
requiring  material  represented  by  29f — M. 

Upon  the  upper  chord,  we  have  the  horizontal  action 
ij  andjgf,  producing  compression  equal  to  30z0"^  upon 

jk.     Add  for  horizontal  action  of  ek  and  kg,  IQw" 
making  40w"-  =stress  of  kl.      Again,   add  4w"  for 

horizontal  action  of  If  and  Id,  and  we  have  44i07/-  = 
J  •» 

thrust  of  Im. 

Thus,  we  have  for  the  whofe  upper  chord,  184v;"^ 
=  aggregate  stress  upon  sections  of  the  common  length 
equal  to  h.  Hence,  representative-  for  material  = 


60 


BRIDGE  BUILDING. 


Aggregate  for  whole  Truss. 


Material  under  Compression. 
Chord,  (2 


Diagonals,  ...  (3?-  +  3f  I?)M 
End  braces,...  (6--+6y)M 


Total, 


Under  Tension. 


Chord 


Diagonals,...  (6f^  +  6?0)ai 
Verticals,  ..... 


Total, 


(367|-f  94My 


Making  A  =  v  =  1,  Comp.  45.714M.     Ten.  =  45.714M. 

Grand  total,  91.428M. 

"We  have  here  a  little  over  3  per  cent  less  actiow  upon 
material,  than  in  case  of  truss  Fig.  12,  with  verticals. 
The  difference  is  a  little  less  than  was  shown  in  my 
original  analysis,  that  heing  based  on  trusses  loaded 
at  the  upper,  and  this,  at  the  lower  chord ;  the  former 
giving  a  trifle  more  action  for  the  truss  with  verticals, 
and  a  trifle  less  for  the  other. 

Moreover,  the  difference  was  made  to  show  greater 
still,  by  assuming  that  deductions  might  be  made  on 
account  of  certain  diagonals  being  liable  to  two  kinds 
of  action.  For  instance,  it  was  supposed  that  a  mem 
ber  formed  to  sustain  a  considerable  tension  stress, 
might  also  sustain  a  small  compressive  force  without 
additional  material  (not  at  the  same  time,  of  course), 
which  is  undoubtedly  the  case,  on  certain  occasions  ; 
especially  in  the  use  of  wooden  trusses.  This  would 
give  still  greater  apparent  advantage  to  truss  13,  with 
regard  to  economy  of  material. 

XL VII.  There  is,  however,  another  view  as  to  the 
action  of  load  upon  truss  Fig.  13,  which  may  modify 
the  results  above  shown  to  a  small  extent. 


TRAPEZOID  WITHOUT  VERTICALS.  Gl 

If  we  strike  out  the  diagonals  cm  and  me,  and  also 
dl  and  (/",  all  the  determinate  forces  necessary  to  sustain 
uniform  weights  at  the  nodes  of  the  lower  chord, 
would  be  exerted  by  remaining  members,  although  we 
have  assigned  to  those  members,  each,  the  sustaining 
of  weight  equal  to  2w"  under  the  full  load,  and  twice 
that  weight  under  certain  conditions  of  partial  load  ; 
and  it  is  quite  certain  that  they  are  necessary  to  the 
stability  of  the  truss  when  partially  loaded.  But  with 
both  halves  loaded  uniformly,  the  weight  upon  each 
half  could  be  transferred  to  the  nearest  abutment,  pro 
ducing  equal  thrust  in  both  directions  upon  the  central 
portion  of  the^  upper,  and  equal  tension  in  opposite  di 
rections  upon  the  lower  chord  ;  whereas,  with  one-half 
loaded,  there  is  no  means  by  which  the  pressure  due 
at  the  farther  abutment  could  be  transferred  past  the 
centre,  without  oblique  members  in  the  centre  panel. 
Still,  which  mode  of  action  takes  place  under  the  uni 
form  load,  when  the  diagonals  are  in  place,  is  a  matter 
involved  in  a  degree  of  uncertainty.  If  the  centre  dia 
gonals  do  not  act,  under  the  uniform  load,  then  ek  and 
fj  must  sustain  each  7w",  instead  of  6z0"  for  the  former, 
and  9w"  for  the  latter,  as  above  estimated.  Also,  kg 
would  sustain  lw"  by  thrust,  and  different  results 
would  be  produced  as  to  stresses  of  various  parts  of 
upper  and  lower  chords. 

The  maximum  stress  for  ek  andefo,  and  for  nb  kg,  would 
be  7*0"^  instead  of  610''-,  as  found  above,  and  would 

V  V 

occur  under  the  full,  instead  of  the  partial  load.  The 
tension  of  gj  arid  06,  also,  would  be  increased  to  14w/'. 
The  weight  sustained  by  fj,  would  be  only  Iw"  under 
the  full  load,  though  liable  to  the  same  maximum 
weight  of  W,  under  a  partial  load. 


62  BRIDGE  BUILDING. 

For  the  lower  chord,  we  should  have  the  same  co 
efficient,  (21)  ofw"-  to  express  the  tension  of  ab  and  ig, 
28  for  be,  35  (a  decrease),  for  cd,  and  42  for  de. 

For  upper  chord,  the  co-efficients  of  w"-  would  be 
28  for  on  and  kj,  and  42  for  the  three  middle  sections; 
no  action  being  imparted  by  diagonals  at  m  and  I. 

XLVIII.  This  uncertainty  of  action  has  no  place  in 
trusses  of  an  even  number  of  panels,  as  in  such  cases, 
no  transfer  of  the  action  of  weight  can  be  supposed  to 
take  place  past  the  centre,  under  a  uniform  load,  with 
out  involving  the  absurdity  of  supposing  the  same 
member  to  carry  weight  by  tension  aiid  compression 
at  the  same  time;  except,  however,  that  in  case  of 
diagonals  crossing  two  panels,  or  having  a  horizontal 
reach  equal  to  twice  the  space  between  nodes  of  the 
chords,  there  will  be  diagonals  filling  the  same  condi 
tion  of  crossing  in  the  centre  of  the  truss,  both  vertically 
and  longitudinally,  as  in  Fig.  13. 

We  may  obviate  mostly,  any  mischief  liable  to  result 
in  cases  of  the  kind  under  consideration,  by  estimating 
the  stresses  upon  the  several  parts  under  both  hypo 
theses,  and  taking  for  each  member  the  highest  estimate, 
which  will  mostly  meet  all  contingencies.  Estimating 
action  upon  truss  13  in  this  manner,  we  obtain  the 
following  representative  expressions  for  material : 


Compression. 


Chord, 26^-— XM 

Diagonals, (4--  -f  4vM 

End  braces,....     6— 

v 


i\h 


Total,  (86^-  +  10w)M 


Tension. 

Chord, SO^X      M 

Diagonals,...  (6= — 
Verticals, 4i/M 


Total,   (37  —  10|v)M 


TRAPEZOIDAL  TRUSS. —  DECUSSATION.  63 

Making  h  =  v  =  1.  These  expressions  give,  Compres 
sion  material  =  46.855M  +  Tension  do,  47.714M  =  total 
94,57iM. 

This  shows  an  aggregate  amount  of  compression  and 
tension  action,  identical  with  that  of  truss  Fig.  12, 
[XLIII.] 

DECUSSATION  AND  NON-DECUSSATION. 

XLIX.  The  elasticity  of  materials  affords  a  means 
of  answering  the  question  as  to  decussation  of  forces 
through  diagonals  crossing  in  the  centre  of  the  truss, 
vertically  and  longitudinally  (as  in  Fig.  13),  in  specific 
cases.  But  the  results  will  vary  in  trusses  of  different 
numbers  of  panels,  and  different  inclinations  of  diago 
nals. 

Suppose  the  truss  Fig.  13  to  be  so  proportioned  that 
the  maximum  stresses  of  the  several  parts  and  members, 
will  produce  change  of  length  equal  to  E,  multiplied 
by  the  lengths  of  parts  respectively ;  the  vertical  ob, 
=  i',  being  the  unit  of  length.  Then,  the  truss  being 
uniformly  and  fully  loaded,  and  the  chords  being  under 
their  maximum  stress,  the  upper  chord  is  contracted, 
and  the  lower  one  extended  at  a  uniform  degree  ;  and, 
if  the  diagonals  be  unchanged  in  length,  their  vertical 
and  horizontal  reaches  have  not  been  changed  by  the 
change  in  length  of  chords.  Hence,  the  distance  be 
tween  chords  is  not  altered  by  change  in  their  length. 
But  the  diagonals  being  under  stress,  by  which  some 
are  extended  and  others  contracted,  according  to  the 
stress  they  are  under,  as  compared  with  their  maximum 
stresses  respectively,  the  nodes  of  the  chords  are  al 
lowed  to  settle  to  positions  below  what  they  are  brought 
to  by  the  mere  change  in  lengths  of  chords. 


64  BRIDGE  BUILDING. 

Hence,  the  panels  are  (generally)  thrown  into  more 
or  less  obliquity  of  form,  in  consequence  of  inequality 
in  length  of  diagonals  in  the  same  panel.  But  the 
centre  panel  can  not  assume  obliquity,  because  any 
tendency  of  forces  to  change  the  length  of  one  dia 
gonal,  is  attended  by  a  like  tendency  of  equal  forces  to 
produce  exactly  the  same  change  in  the  other ;  so  that 
the  vertical  reaches  of  both  must  suffer  the  same  change, 
if  any,  and  both  must  be  under  tension  or  compression, 
according  as  the  acting  forces  tend  to  bring  the  chords 
at  the  centre,  nigher  together  or  farther  apart. 

Now,  the  forces  produced  by  the  load  being  all  con 
centrated  at  the  points  o  and  j  (Fig.  13),  the  point  d  is 
depressed  with  respect  to  0,  by  the  extension  of  ob  and 
?i6?,  and  by  the  compression  of  bn.  Hence,  assuming 
decussation  to  have  place,  giving  tension  to  the  diagonals 
dl  and  me,  equal  to  what  is  due  to  a  weight  of  1w",  ob  is 
under  maximum  tension  and  gives  depression  equal  to  E, 
to  the  point  6,  —  bn  and  nd  are  under  §  maximum  stress, 
and  give  depression,  each  equal  to  f  E  XD2*  = 
(1.666/i2  4-  1.666)  E,  for  the  two  (D  representing  length 
of  diagonals,  =v/F+I).  Then,  adding  IE  for  effect 
of  ob,  we  obtain  (1.666A2  +  2.666)  E,  =  depression  of 
point  d. 

The  point  m  is  depressed  by  extension  of  oc  under  a 
maximum  stress,  giving  an  amount  equal  to  D2E  = 
(A2  -f  1)E.  Also,  by  compression  of  cm  under  one-half 
maximum  stress,  to  the  extent  of  (JA2  -f  J)E.  Hence, 
depression  of  point  m  =  (1  J/i2  +  1 J)  E. 

This  shows  the  point  d  to  be  depressed  more  than 
w,  by  (1.666  A2  4-  2.666)  E  — (1.5/t2  +  1.5)E  -(0.166A2  + 


*Let  the  diagonals  bd  and  Bd,  of  two  rectangular  panels  ac  and  Ac, 
Fig.  14  (c  and  d,  being  fixed  points),  be  exposed  to  tension  in  propor 
tion  to  their  respective  cross-sections,  receiving  each  thereby,  extension 


TRAPEZOIDAL  TRUSS. —  DECUSSATION. 


65 


1.166)  E,  and  the  spaces  md  and  le  to  be  increased  to 
that  extent;  of  course  producing  tension  upon  c/land  me. 

Now,  by  hypothesis,  these  diagonals  are  under  the 
weight  of  2w"y  giving  half  maximum  stress,  and  requir 
ing  an  increase  of  vertical  reach,  equal  to  (%h2  -f  J)  E. 
If  then,  we  give  such  a  value  to  A,  as  will  make  the 
last  co-efficient  of  E  equal  to  the  one  above,  it  will 
show  that  the  chords  have  receded  just  enough  to  give 
the  assumed  tension  to  dl  and  me,  and  the  decussation 
is  a  demonstrated  fact.  To  find  the  value  of  A,  pro- 
ducingthis result,  make,.5A2  -f  .5  =  .166A2  +  l,166,and 
we  deduce  ,333A2  =*  .666  ;  whence  h  =  v"2. 

But  this  requires  too  great  an  inclination  of  diagonals, 
and  a  less  value  of  A,  gives  a  space  from  d  to  m  too 
great  for  the  supposed  tension  of  dl  and  me.  Making 
h  =  1  =  v,  we  have  increase  of  distance  from  d  to  m  » 
1.333E,  requiring  a  weight  of  2.666*0",  to  stretch  dl 
down  to  the  point  d.  But  as  no  weight  or  stress  can 
be  added  to  the  2io"  assigned  to  dl  and  me,  without  af- 


equal  to  b'e  and  B'E,  respectively.     This  will  cause  the   points  b  and 
B  to  drop  to  b'  and  B',  in  ab  and  AB  produced.    Join  b  e  and  BE. 

Then,  the  infinitesimal  triangles  bb'e  and 
BB'E,  right-angled  at  e  and  E,  are  essentially  ^  I(3-  14. 

similar,  respectively  to  the  triangles  db  a 
dBA.     Hence,  the  following  relations  : 

(1).     bb'  :  b'e  :  :  bd  :  ab,         and 

(2).    BB'  :  B'E  :  :  Bd  :  ab. 
whence,     bb'  X  ab  =  b'e  X  bd,  and 


From  these  two  equations  we  derive  — . 

(3).    bb'  X  ab  :  BB'  X  ab :  :  b'e  X  bd : 
B'E  X  Bd. 

But,  by  the  law  of  elasticity 

(4).  b'e  :  B'E  :  :  bd  :  Bd  ;  whence, 

(5).  b'e  X  bd  :  B'E  X  Bd  :  :  bd2  :  Bd2. 

Hence  dividing  the  first  ratio  of  proportion  (3)  by  ab,  and  substitu 
ting  for  the  last  ratio  of  (3),  its  equivalent  found  in  (5),  we  have 

(«).  bb'  :  BB'  :  :  bd* :  Bd2. 

Hence  the  depression  due  to  the  extension  of  a  diagonal  retainincr 
the  same  vertical  reach,  is  as  the  stress  (per  square  inch),  sustained*, 
multiplied  by  the  square  of  the  length  of  diagonal. 

9 


66  BRIDGE  BUILDING. 

fecting  all  the  5  members  contributing  to  the  depression 
of  the  points  d  and  m,  and  in  all  cases,  so  as  to  dimin 
ish  the  elongation  of  distance  between  d  and  m,  it  is 
reasonable  to  conclude  that  by  assigning  some  J,  or 
thereabouts,  of  the  extra  weight  of  .666?0"  required  on 
dl  alone,  it  would,  by  affecting  the  whole  5  members, 
be  sufficient  to  correct  the  error.  Let  us,  then,  assume 
that  dl  and  me  sustain  2.15i0",  instead  of  2*0"  as  by  pre 
vious  supposition.  This  change  requires  reduction  of 
weight  upon  dn,  nb  and  bo,  from  5*0"  to  4.85*0"  for  the 
two  former,  and  from  12*0"  to  11.85*#"  for  bo.  Also 
an  increase  of  weight  on  we  and  co,  to  2.1  Sic"  on  me, 


and  to  9.15i0"  on  co.  Then  bo  sustains  —  —  of  the 
maximum,  and  gives  depression  «-~-E  =  .9875E 

bn  and  nd,  sustaining  -~  of  the  maximum,    give  de 
pression  for  the  two,  equal  to  3.233E,  making  4.2205E 
=  whole  depression  of  point  d. 
With  regard  to  the  point  m,  we  have  the  maximum 

2  15 
stress  on  oc,  giving  depression  equal  to  2E,  and   V-  Of 

the  maximum  on  me,  giving  depression  =  1.0T5E, 
making  a  total  of  3.075E  for  the  point  m.  Hence,  the 
elongation  of  the  space  dm,  equals  (4.2205  —  3.075)  E, 
=  1.145E,  whereas  2.15*0"  upon  dl,  increases  its  vertical 
reach  by  only  1.075E.  This  shows  that  dl  sustains  still 
a  little  more  than  2.1  5*0".  On  the  other  hand  if  we 
assume  a  weight  of  2.2*0"  on  dl,  we  obtain  the  opposite 
result,  showing  that  dl  sustains  less  than  2.2*0",  and 
hence  the  actual  amount  must  be  between  2.15*0"  and 


We  conclude  then,  that  dl  and  me  are  mot  inactive 
under  the  full  load  of  the  truss,  but  on  the  contrary, 
they  sustain,  in  this  case,  even  more  than  the  decussa- 
tion  theory  assigns  to  them.  We  learn,  moreover,  that 


TRAPEZOIDAL  TRUSS. —  DECUSSATION.  67 

the  question  is  affected  by  the  horizontal  reach  of  the 
diagonal,  or  the  value  of  h.  And,  since  in  this  case, 
the  point  d  being  depressed  by  action  upon  3  members, 
and  the  point  m  by  action  upon  only  2,  we  have  an  elon 
gation  of  space  between  dandm  requiring  more  than  the 
theoretical  stress  upon  centre  diagonals,  it  is  natural  to 
conclude,  that,  in  case  of  a  greater  number  of  panels, 
nine,  for  instance,  where  4  members  contribute  to  the 
depression  of  the  upper,  and  only  three  to  that  of  the  lower 
chord  at  the  centre,  the  increase  of  distance  between 
chords,  would  be  less  than  that  required  to  give  the  theo 
retical  stress  upon  diagonals  in  the  centre  panel ;  and, 
such  is  found  to  be  the  case.  In  a  nine  panel  truss  on  the 
plan  of  Fig.  13,  the  increase  of  distance  between  chords, 
due  to  the  stresses  assigned  by  the  decussation  theory,  is 
only  about  one-third  of  what  would  be  required  to 
give  the  centre  diagonals  the  stress  assigned  them. 
Hence  in  this  case  there  is  less  decussation  than  the 
theory  requires  ;  and,  one  or  two  trials,  by  ^assigning 
different  weights  as  sustained  by  centre  diagonals,  in 
the  manner  pointed  out  above,  would  enable  a  near 
approxination  to  the  actual  amount  of  decussation  to 
be  arrived  at,  in  the  case  of  the  nine  panel  truss,  or 
any  other. 

Let  us  take  one  more  view  of  this  matter,  by  assum 
ing  no  action  by  centre  diagonals,  under  the  full  load. 
Then  cm  (Fig.  13),  is  also  out  of  action,  and  oc  alone, 
under  J  maximum  stress,  contributes  to  the  depression 
of  point  m,  giving  depression  equal  to  2x^E,  =  1.55E, 
(assuming  h  =  v). 

The  point  d  is  depressed  by  the  maximum  change  of 
two  obliques,  and  one  vertical,  giving  depression  =  5E. 
Therefore  the  distance  md,  is  increased  by  (5  — 1.55)  E, 
=*  3.45E.  Hence  dl  and  me  must  be  elongated  by  1.725 


68  BRIDGE  BUILDING. 

times  the  amount  due  to  the  maximum  stress,  in  order 
to  escape  action.  Suppose  the  member  to  be  of  wrought 
iron,  proportioned  to  a  maximum  stress  of  10,000ft)  to 
the  square  inch.  Then,  the  extension  due  to  17250ft) 
to  the  inch,  is  about  seVVoVVo  x  length  "*  .00069  X 
length,  and  if  length  «—  15  feet,  tne  extension  is  equal 
to  .00069x15,  =  .01035  ft.  or,  say  J  inch. 

Hence,  in  a  7  panel  truss,  as  represented  in  Fig.  13, 
with  h  =  v9  if  the  diagonals  in  the  middle  panel  be 
slack,  by  J  inch  in  15  feet  of  length,  no  decussation 
will  take  place,  and  the  centre  diagonals  will  be  inactive, 
under  the  full  load  of  the  truss.  If  those  members  have 
less  than  that  degree  of  slackness,  they  will  be  in  action 
in  such  circumstances. 

It  would  be  a  very  badly  adjusted  piece  of  work  in 
which  such  a  degree  of  slackness  should  occur,  and  we 
may  fairly  conclude,  that  the  centre  diagonals,  in  this 
class  of  trusses,  are  never  entirely  inactive. 

But  the  quantity  E,  is  so  very  small,  with  any  kind 
of  material,  and  with  any  co-efficient  that  may  affect 
it,  in  practice,  that  a  slight  inaccuracy  of  adjust 
ment,  may  so  change  the  practical  form  the  theoretical 
results  deduced  by  calculation,  as  to  decussation,  as  to 
render  the  latter  of  no  great  practical  reliability. 
Hence,  after  all,  perhaps  the  most  unexceptionable 
course,  in  this  regard  is,  to  follow  the  rule  given  before 
[XLVIII],  of  estimating  stresses  on  both  hypotheses, 
and  taking  the  highest  estimate  for  each  part. 

Now,  perhaps,  this  subject  has  been  discussed  at 
greater  length  than  its  practical  importance  demanded, 
considering  the  small  percentage  of  error  liable  to  oc 
cur  in  any  case  ;  but  with  regard  to  this,  as  well  as  to 
other  matters,  it  is  well  to  know,  what  may  be  known 


TRAPEZOIDAL  TRUSS. — WARREN  GIRDER.        69 

without  inconvenient  or  unreasonable  effort  at  investi 
gation. 

THE  WARREN  GIRDER. 

L.  There  is  another  form  of  truss  operating  upon 
the  same  principle  as  truss  Fig.  13,  in  which  one  set 
of  oblique  members  is  left  out,  so  that  only  one  diago 
nal  remains  to  each  panel.  The  diagonals  meet  and 
connect  with  one  another  and  with  the  chords,  forming 
alternate  nodes  at  the  upper  and  lower  chords.  This 
truss,  represented  in  Fig.  15,  requires  an  even  number 
of  panels  that  the  two  half-trusses  may  be  symmetrical. 

This  is  an  extension  of  truss  Fig.  5,  with  tension 
verticals  for  suspending  floor  beams  from  the  upper 
nodes,  when  the  travel-way  is  along  the  lower  chord, 
and  thrust  verticals  ascending  from  the  lower  nodes, 
in  the  case  of  what  are  technically  called  deck-bridges.* 

We  compute  the  stresses  of  the  members  of  this 
truss,  by  placing  the  figures  1,  2,  3,  etc.,  over  the 
diagram  as  in  preceding  cases,  #nd  from  a  second  line 
or  series  of  figures,  by  adding  all  those  in  the  first 
series,  as  in  case  of  truss  Fig.  12,  because  each  weight 
tends  to  act  upon  every  diagonal.  Each  figure  in  the 
second  line,  fs  the  co-efficient  of  w"  in  the  expression 
of  the  greatest  weight  transferred  to  the  right  hand 
abutment,  through  the  diagonal  crossing  the  panel 
next  on  the  right  hand  of  the  figure  ;  and  the  action  is 
tension  or  thrust,  according  as  the  diagonal  ascends  or 
descends  toward  the  right.  Thus,  the  Fig.  6  over  o, 
indicates  that  6w"  is  the  greatest  weight  acting  by  thrust 
upon  oe,  while  10  over  the  point  e,  indicates  10w''  as  the 
maximum  weight  acting  by  tension  upon  em.  These 

*The  author  built  several  small  bridges  upon  this  plan,  to  carry  a 
rail  road  track  over  common  highways,  in  1849  or  1850,  believed  to 
have  been  the  first  application  of  this  form  of  truss. 


70 


BRIDGE  BUILDING. 


figures  only  indicate  weight  transferred  from  left  to 
right,  and  it  is  evident  that  the  same  weights  in  a  re 
versed  order,  are  transferred  from  right  to  left,  through 
the  same  diagonals.  Hence,  a  third  series  of  figures 
under  the  second,  composed  of  the  same  figures  in  a 
reversed  o*rder,  shows  the  weights  carried  by  the  seve 
ral  diagonals  from  right  to  left.  The  figures  in  the 
third  line,  show  the  weights  acting  on  diagonals  next 
on  the  left  of  respective  figures.  It  will  be  seen  also, 
that  the  figures  under  odd  numbers  of  the  upper  line, 

FIG.  15. 


c          d          e         f         g          i  j 

indicate  weights  acting  by  thrust,  and  those  under  even 
numbers,  by  tension.  The  figures  6  and  15  over  o,  in 
dicate  6w"  acting  on  oe,  and  15?fl",  on  oc,  both  by 
thrust.  Again  3  and  21  under  2,  indicate  3w"  acting 
on  co,  and  2lw"  upon  cq,  both  by  tension?  The  figure 
28  at  the  right  and  left,  under  1  and  7,  indicate  2Sw" 
acting  by  thrust  upon  aq  and  jk. 

Now  if  we  add  all  the  figures  in  the  second  and  third 
lines  standing  under  odd  numbers  of  the  upper  line, 
we  obtain  the  co-efficient  of  w"  for  the  aggregate  maxi 
mum  weights  acting  by  thrust  upon  oblique  members, 
while  the  sum  of  all  the  figures  in  like  manner,  under 
even  numbers,  forms  the  co-efficient  of  w"  for  the  ag 
gregate  maximum  weights  acting  by  tension  upon  ob 
liques.  The  former  gives  100w",=12.5w  for  compres 
sion,  and  the  latter,  68u?",=»8.5i0,  for  tension.  Hence, 


TRAPEZOIDAL  TRUSS.— WARREN  GIRDER.        71 

making  A=r=l,  we  have  as  expressions  for  amount  of 
thrust  and  tension  action  upon  material  in  oblique  mem 
bers,  25M  for  thrust  and  17M  for  tension. 

One  half  of  the  lower  chord  obviously  sustains  a 
stress  of  28  w",  equal  to  horizontal  thrust  of  the  end 
braces,  and  the  other  half,  60w",=  horizontal  action  of 
aq,  qc  and  co  (under  full  uniform  load),  at  one  end,  and 
of  corresponding  diagonals  at  the  other  end,  giving  re 
quired  material  for  chord  equal  to  44M. 

The  compression  of  the  upper  chord,  equals  the  hori 
zontal  thrust  and  pull  of  aq  and  qe,=  48w",  for  f  of  its 
length,  with  the  addition  of  ~L2w"  for  horizontal  thrust 
of  co,  and  4w"  for  pull  of  oe,  making  Q±w"  for  the  two 
middle  panels.  Hence  expression  for  material  is  40M. 
The  verticals  obviously  require  tension  material  equal 
to  4M,  and  the  aggregate  for  the  truss,  is, 

For  Compression.  For  Tension. 

Chord, 40M         Chord, 44M 

Obliques, 25M         Diagonals, 17tf 

Verticals,  4M 


Total, 65M    Total, 65M 

A  corresponding  truss  with  2  diagonals  in  each 
panel,  on  the  plan  of  Fig.  13,  shows  the  same  expres 
sions  for  materials,  or  amount  of  action  of  both  kinds, 
item  for  item,  and  any  advantage  possessed  by  either 
plan,  must  depend  essentially  upon  the  more  advan 
tageous  action  of  compression  material. 

Truss  Fig.  15,  has  fewer  intermediate  thrust  diagonals, 
and  greater  concentration  of  weight  upon  them  ;  which 
is  favorable;  while  in  the  other,  the  diagonals  crossing 
one  another,  are  enabled  to  afford  mutual  support 
laterally,  in  certain  modes  of  construction. 


72  BRIDGE  BUILDING. 

The  upper  chord  in  Fig.  15,  acts  at  a  decided  disad 
vantage,  in  having  no  vertical  support  for  a  length  of 
2  panel  widths,  unless  it  be  especially  provided  at  ad 
ditional  expense.  As  a  deck  bridge,  with  struts,  or 
posts  atp,  n,  I,  and  lateral  tying  and  bracing,  the  truss 
may  answer  an  excellent  purpose.  But  even  in  that 
case,  it  can  scarcely  be  considered  as  preferable  to  the 
truss  with  a  double  system  of  diagonals. 

The  Ohio  river  bridge  at  Louisville,  Ky.,  has  its  long 
spans  (about  400  ft),  constructed  upon  the  plan  of  Fig. 
15,  and  no  plan  which  we  have  considered,  shows  a 
less  amount  of  action  upon  material.  These  are  believed 
to  be  the  longest  spans  of  Truss  Bridging  in  the  country. 

An  eight-panel  truss  upon  the  plan  of  Fig.  12,  gives 
the  following  expressions  for  amount  of  material. 

Compression.  Tension. 

Chord,  43M         Chord, 4lM 

Ends,  .14M        Diagonals, 28M 

Verticals, TM        Verticals, 2M 


64M  7lM 

This  indicates  a  difference  of  nearly  4  per  cent,  as 
to  amount  of  action  upon  material,  in  favor  of  the  truss 
without  vertical  members,  generally  speaking;  i.  e.  in 
which  there  is  no  regular  transfer  of  action  from  one  to 
another,  between  diagonal  and  vertical  members,  as  in 
truss  Fig.  12. 

This  advantage  is  made  still  larger  in  certain  modes 
of  construction,  by  the  circumstance  that  the  same 
members,  in  trusses  13  and  15,  may  sometimes  act  by 
tension  and  thrust,  on  diiferent  occasions,  without  any 
more  material  than  would  be  required  to  act  in  one 
direction  only. 


FINCK  TRUSS.  73 

LI.  It  may  be  proper  in  this  place,  to  refer  to  still 
another  form  of  trussing,  which  has  enjoyed  a  degree 
of  popular  favor,  and  which  differs  somewhat  from 
any  we  have  hitherto  considered.  The  plan  is  seen  in 
outline,  in  Fig.  16.  Each  weight  is  sustained  primarily 
by  a  pair  of  equally  inclined  tension  members,  and 
thereby  transferred  either  to  the  king  posts  standing 
upon  the  abutments,  or,  to  posts  sustained  by  other 
pairs  of  equally  inclined  suspension  rods  of  greater 
horizontal  reach;  which  in  turn,  transfer  a  part  to 
king  posts,  and  another  part  to  a  post  sustained  by 
obliques  of  still  greater  reach,  until  finally,  the  whole 
remaining  weight  is  brought  to  bear  upon  the  abut 
ments  by  a  single  pair  of  obliques,  reaching  from  the 
centre  to  each  abutment. 

FIG.  16. 
THE  FINCK  TRUSS. 


In  Fig.  16,  are  represented  three  different  lengths  of 
obliques,  in  number,  inversely  as  the  respective  hori 
zontal  reaches.  The  first  set  contains  8  pieces  reaching 
horizontally  across  one  panel,  and  sustaining  each  \w. 
The  next  longer  set,  of  four  pieces,  reach  across  two 
panels,  and  sustain  eachlw;;  one-half  applied  directly, 
and  the  other,  through  posts  and  short  diagonals.  The 
third  and  longest  set,  contains  but  two  pieces,  reach 
across  four  panels,  and  sustain  together  ±w\  of  which  Iw 
is  applied  directly,  Iw  through  two  short  diagonals? 
and  2w  through  two  intermediates. 

Now,  as  each  set  sustains  the  same  aggregate 
weight,  namely  4w9  the  material  in  each  set,  will 
10 


74  BRIDGE  BUILDING. 

be  represented  by  this  weight  multiplied  by  the 
square  of  the  lengths  respectively,  and  divided  by  v  : 
and,  making  k  =  v  =  1,  the  squares  of  respective 
lengths  are  2,  5  and  17,  which  added  together  and  mul 
tiplied  by  4w?,  and  w  changed  to  M,  gives  96M=amount 
of  material  in  tension  obliques,  the  only  tension  mem 
bers  in  the  truss. 

The  upper  chord  sustains  compression  equal  to  the 
horizontal  pull  of  one  oblique  member  of  each  class, 
obviously  equal  to  lOJw,  with  length  =  8.  Hence,  re 
quired  material  equals  84M.  End  posts  sustain  to 
gether,  *7w,  centre  post  810,  and  the  two  at  the  quarters, 
one  w  each,  in  all  12ic,  and  the  representative  for  mate 
rial  is  12M  ;  whence  the  total  for  thrust  material  is  96M, 
making  a  grand  total  of  thrust  and  tension  material= 
192M. 

The  8  panels  trapezoid  with  verticals,  requires,...  135M 
Do  "  "  without  verticals, 130M 

This  comparison  exhibits  an  amount  of  action  in 
case  of  the  first  (Fig.  16),  which,  considering  that  it 
possesses  no  apparent  advantage  as  to  the  efficient 
working  of  compression  material,  would  seem  to  ex 
clude  it,  practically,  from  the  list  of  available  plans  of 
construction. 

DISTINCTIVE  CHARACTERISTICS  OF  THE  ARCH. 

LIT.  We  have  seen  that  all  heavy  bodies  near  the 
earth's  surface  (except  when  falling  by  gravity  or 
ascending  by  previous  impulse),  exert  a  pressure  upon 
the  earth  equal  to  their  respective  weights.  We  have 
also  seen  that  the  object  of  a  bridge,  in  general,  is,  to 
sustain  bodies  over  void  spaces,  by  transferring  the 
pressure  exerted  by  them  upon  the  earth,  from  the 


THE  ARCH  TRUSS.  75 

points  immediately  beneath  them,  to  points  at  greater 
or  less  horizontal  distances  therefrom. 

We  have,  moreover,  seen  that  this  horizontal  trans 
fer  of  pressure  can  only  be  effected  by  oblique  forces 
(neither  exactly  horizontal  nor  exactly  vertical),  and 
have  discussed  and  compared,  in  a  general  way,  various 
combinations  of  members,  capable  of  effecting  this 
horizontal  transfer  of  pressure. 

But,  without  going  into  unnecessary  recapitulation, 
we  find  two  or  three  styles  of  trussing,  possessing  more 
or  less  distinctive  features,  which  promise  decidedly 
more  economical  and  satisfactory  results  than  any 
others ;  and,  to  make  the  properties  and  principles  of 
action  of  the  best  and  most  promising  plans  as  tho 
roughly  understood  as  may  be  within  the  proposed  limits 
of  this  work,  will  form  a  prominent  object  in  the  discus 
sions  of  succeeding  pages. 

The  distinctive  feature  of  the  arch,  as  a  sustaining 
structure,  consists  in  the  fact  that  all  the  oblique  action 
required  to  sustain  a  uniformly  distributed  load,  is  ex 
erted  by  a  single  member  of  constantly  varying  ob 
liquity  from  centre  to  ends  ;  each  section  sustaining 
all  the  weight  between  itself  and  the  centre,  or  crown 
of  the  arch,  and  none  of  the  weight  from  the  section 
to  the  end  ;  so  that  the  weight  sustained  at  any  point, 
is  as  the  horizontal  distance  of  that  point  from  the 
centre.  Consequently  (the  arch  being  supposed  in 
equilibrio  under  a  uniform  horizontal  load),  the  hori 
zontal  thrust  at  all  points  must  be  the  same,  and  the 
inclination  of  the  tangent  at  any  point  should  be  such 
that  the  square  of  the  sine,  divided  by  the  cosine  of  in 
clination  (from  the  vertical),  may  give  a  constant  quo 
tient.  For,  regarding  each  indefinitely  short  section 
of  the  arch  as  a  brace  coinciding  with  the  tangent  at 


76  BRIDGE  BUILDING. 

/ 
the  point  of  contact,  its  horizontal  thrust  equals  the 

weight  sustained,  multiplied  by  the  horizontal,  and  di 
vided  by  the  vertical  reach  of  the  brace.  But  the 
horizontal  and  vertical  reaches  are  respectively  as  the 
sine  and  cosine  of  the  angle  made  by  the  tangent  with 
the  vertical ;  that  is,  as  ab  and  bd,  Fig.  17,  while  the 

weight  is  also  as  the  sine  «6, 
FIG.  17.  of  the  angle  adb.     Hence,  the 

weight  by  the  '  horizontal 
reach,  is  as  ab2,  or  as  the  square 
of  the  sine  of  adb ;  and  the 
constant  horizontal  thrust  of 
\  the  arch  at  all  points,  is  as 

afca  a&2 

M*    °r>    ^ 
Now  this  condition  is  answered  by  the  parabola,  in 

which  bc  =  cd  =  -J  bd,  and |~  =  J— —constant  C,  whence 
ab2  =  cb  x  constant  2(7,  which  is  the  equation  of  the 
parabola. 

This  quality  of  the  arch  truss,  allowing  nearly  all  of 
the  compressive  action  to  be  concentrated  upon  almost 
the  least  possible  length,  and  consequently,  enabling 
the  thrust  material  to  work  at  better  advantage  than 
in  plans  where  this  action  is  more  distributed,  and  acts 
upon  a  greater  number  and  length  of  thrust  members, 
enables  it  to  maintain  a  more  successful  competition 
with  other  plans  than  we  might  be  led  to  expect,  in 
view  of  the  greater  amount  of  action  upon  materials 
in  the  arch  truss,  than  what  is  shown  in  trusses  with 
parallel  chords.  Hence,  we  should  not  too  hastily 
come  to  a  conclusion  unfavorable  to  the  arch  truss,  on 
account  of  the  apparent  disadvantage  it  labors  under, 
as  to  amount  of  action  upon  material.  These  apparent 
disadvantages  are  frequently  overbalanced  by  advan- 


WEIGHT  OF  STRUCTURE.  77 

tages  of  a  practical  character,  which  can  not  readily  be 
reduced  to  measurement  and  calculation. 

The  preceding  general  comparisons  are  tobe  regarded 
only  as  approximations,  and  should  not  be  taken  as 
conclusive  evidence  of  the  superiority  or  otherwise,  of 
any  plan,  except  in  case  of  very  considerable  difference 
in  amount  of  action,  with  little  or  no  probable  advan 
tage  in  regard  to  efficient  action  of  material. 


EFFECTS  OF  WEIGHT  OF  STRUCTURE. 

LIII.  In  preceding  analyses,  and  estimates  of 
stresses  upon  the  various  members  in  bridge  trusses, 
regard  has  only  been  had  to  the  effects  of  movable  load, 
which  may  be  placed  upon,  or  removed  from  the  struct 
ure,  producing  more  or  less  varying  strains  upon  its 
several  parts. 

But  the  materials  composing  the  structure,  evidently 
act  in  a  similar  manner  with  the  movable  load,  in  pro 
ducing  stress  upon  its  members ;  the  only  difference 
being,  that  the  weight  of  structure  is  constant,  always 
exerting  or  tending  to  exert  the  same  influence  upon 
the  members,  instead  of  a  varying  action,  such  as  that 
produced  by  the  movable  load.  In  order,  therefore,  to 
know  the  absolute  stress  to  which  any  member  is  liable, 
and  thereby  to  be  able  to  give  it  the  required  strength 
and  proportions,  we  have  to  add  the  stresses  due  to 
constant  and  occasional  loads  together. 

The  weight  of  structure  evidently  acts  upon  the 
truss  in  the  same  manner  as  if  it  were  concentrated  at 
the  nodes  along  the  upper  and  lower  chords,  and  of 
the  arch,  in  case  of  the  arch  truss.  And,  since  much 
the  larger  proportion  of  it  acts  at  the  points  where  the 


78  BRIDGE  BUILDING. 

movable  load  is  applied,  if  we  regard  the  whole  as 
acting  at  those  points,  the  results  obtained  as  to  stresses 
produced  by  it,  will  be  sufficiently  accurate  for  ordi 
nary  practice.  Still,  more  closely  approximating  results 
may  be  obtained  by  assigning  to  both  upper  and  lower 
nodes,  their  appropriate  shares  cf  weight  sustained,  as 
may  easily  be  done  when  deemed  expedient. 

If  we  divide  the  whole  weight  of  superstructure  sup 
ported  by  a  single  truss,  by  the  number  of  panels,  the 
quotient,  which  we  may  represent  by  w/,  will  show  the 
weight  to  be  assumed  for  each  supporting  point,  on 
account  of  structure ;  and  the  stresses  produced  by  such 
weights,  added  to  the  maximum  stresses  of  the  several 
members,  due  to  the  movable  load,  will  represent  the 
true  absolute  stresses  the  respective  members  are  liable 
to  bear. 

Now,  as  far  as  relates  to  parts  suffering  their  maxi 
mum  stresses  under  the  full  load,  such  as  chords, 
arches,  king  braces,  and  verticals  in  the  arch  truss,  as 
to  their  tension  strain,  we  have  only  to  substitute  TV, 
(=w;-f  wf),  in  place  of  w,  in  expressions  obtained  for 
stresses  due  to  movable  load.  In  other  cases,  w  and 
wr  will  have  each  its  peculiar  and  appropriate  co-effi 
cient. 

The  diagonals  of  the  arch  truss,  are  obviously  not 
affected  by  weight  of  structure,  as  they  are  not  so 
under  full  and  uniform  movable  load.  Moreover,  the 
weight  of  structure  acts  in  constant  opposition  to  the 
compressive  action  of  movable  load  upon  verticals. 
Hence,  in  truss  Fig.  11,  where  we  find  the  varying 
movable  load  gives  a  maximum  compression  upon  the 
longest,  equal  to  %w",  and  upon  the  next  shorter,  equal 
to  2w/',  the  weight  of  structure  diminishes  those  quan 
tities  to  3w" — w',  and  typ" — wf  respectively.  Or,  if  we 


WEIGHT  OF  STRUCTURE. 


79 


would  be  more  exact,  we  may  add  in  both  cases,  the 
weight  of  a  segment  of  the  arch,  which  has  no  tendency 
to  produce  tension  upon  the  verticals  ;  or  we  may  sub 
tract  only  f  or  £  of  w' ;  thus,  3w/'— fz//,  and  2?tf"— fw', 
may  be  taken  to  represent  the  compressive  action  upon 
the  verticals  in  Fig.  11. 


LIY.  In  the  case  of  truss  Fig.  12,  the  only  diagonals 
acting  under  uniform  load,  are  oc9  fj,  nd  and  ek\  the 
two  latter  sustaining,  of  weight  of  structure,  Ii0',  and 
the  two  former,  2i0'.  And,  the  maximum  movable 
weight  borne  by  those  members,  being  [XL]  IQw"  and 
15i0",  the  absolute  maximum  will  be  10z0"+z0'  for  nd 
and  ek,  and  I5w"+2wf  for  oc  andjf)'. 

Now,  if  we  place  the  figure  1  under  d  and  e,  (Fig.  12 
A),  and  the  figure  2  under  c  and/,  and  so  on,  in  case  of 
a  greater  number  of  panels,  to  the  foot  of  the  last  diagonal 
each  way,  inclining  outward  from  the  lower  nodes,  these 
figures  are  obviously,  the  co-efficients  of  w'  to  express 
the  weights  contributed  by  the  material  of  the  stru  - 
ture,  to  the  stresses  of  diagonals  extending  upward  and 
outward  from  the  points  to  which  the  figures  respect 
ively  refer. 

FIG.  12  A. 


1  2 

1  3 

o          n 


8 
6 

ra 


4 

10 

I 


5 
15 

k 


6 
21 

j 


f 


Again,  we  have  seen  [XL],  that  a  certain  condition 
of  the  movable  load,  tends  to  throw  \w"  upon  bn,  and 
another  condition  of  such  load,  tends  to  throw  &w"  upon 


80  BRIDGE  BUILDING. 

cm.  But,  since,  as  we  now  see,  the  weight  of  structure 
tends  to  throw  a  constant  weight  of  2w'  up6n  oc,  which 
is  antagonistic  to  bn,  the  actual  maximum  weight  upon 
6n,  is  lw" — 2w/,  which  will  always  be  a  negative  quan 
tity,  in  practice ;  whence  bn  must  always  be  inactive, 
and  may  be  dispensed  with. 

The  maximum  weight  upon  cm,  as  modified  by 
weight  of  structure,  is  in  like  manner  reduced  to  3w" 
— wf,  which  will  in  practice,  be  either  negative,  or  of 
quite  small  amount.  Hence,  we  have  the  following 
rule :  For  the  absolute  maximum  stresses  of  diagonals 
(in  case  of  parallel-chord  trusses  with  verticals),  we 
add  the  effects  of  weight  of  structure  to  the  maximum 
effects  due  to  variable  load,  where  both  fall  upon  the 
same,  and  subtract  the  former,  in  cases  where  the  two 
forces  fall  upon  counter,  or  antagonistic  diagonals. 

In  case  of  parallel-chord  trusses  without  verticals,  we 
add  the  effects  of  constant  and  variable  load  upon  each 
diagonal,  when  alike,  i.  e.,  when  both  tensile  or  both 
compressive,  and  subtract  the  former  when  the  effects 
are  alike. 


DOUBLE  CANCELLATED  TRUSSES. 

LY.  The  use  of  chords  in  a  truss  being  to  sustain 
the  horizontal  action  (whether  of  thrust  or  tension)  of 
the  oblique  members,  it  follows  that  the  aggregate 
stress  of  chords,  is  equal  to  the  aggregate  horizontal 
action  of  all  the  diagonals  acting  in  either  direction e 
And,  the  horizontal  action  being  obviously  as  the 
number  and  horizontal  reach  directly,  and  as  the  ver 
tical  reach  inversely ;  also,  the  length  of  truss  being  as 


DOUBLE  CANCELATED  TRUSSES.  81 

the  number  and  horizontal  reach  of  diagonals,  while 
the  vertical  reach  is  as  the  depth  of  truss,  it  follows 
that  the  stress  of  chords  is  directly  as  the  length  and 
inversely  as  the  depth  of  truss,  other  conditions  being 
the  same. 

Hence,  if  the  depth  of  truss  be  so  reduced  as  to  make 
the  ratio  of  length  to  depth  indefinitely  large,  the  stress 
and  required  material  of  chords,  become  indefinitely 
large.  On  the  contrary,  if  the  depth  be  indefinitely 
great,  al!hough  the  stress  of  chords  be  ever  so  small 
the  length  and  required  material  for  diagonals  and  ver 
ticals  must  be  indefinitely  large.  It  is  manifest,  then,, 
that  between  these  two  extremes  there  is  a  practical, 
optimum, —  a  certain  ratio  of  length  to  depth  of  trussy 
which',  though  it  may  vary  somewrhat  with  circum 
stances,  will  give  the  best  possible  results  as  to  economy 
of  material  in  the  trass.  This  matter  will  be  taken 
into  consideration  hereafter,  and  is  referred  to  here, 
to  show  the  expediency  of  generally  increasing  the 
depth,  with  increase  of  lengths  in  the  truss. 

Now,  in  trusses  of  considerable  length,  and,  conse 
quently,  depth,  it  becomes  expedient,  in  order  to  avoid 
too  great  a  width  of  panel  (horizontally),  or  an  inclina 
tion  of  diagonals  too  steep  for  economy  of  material  in 
those  members,  to  extend  them  horizontally  across  two 
or  more  panels,  or  spaces  between  consecutive  nodes 
of  the  chords.  In  such  cases,  the  truss  may  be  called 
double  or  treble  cancelated,  according  as  the  diagonals 
cross  two  or  three  panels.  i 

LVL  To  estimate  the  stresses  of  the  members  of 
double  cancelated   trusses  with   vertical   members,  a 
slight  modification   of  the  process  already   described, 
[XL,  &c.],  is  required,  as  follows  : 
11 


82  BRIDGE  BUILDING. 

Having  placed  the  numbers  1,  2,  3,  &c.,  over  the 
nodes  of  the  upper  chord,  as  seen  in  Fig.  18,  place 
under  each  odd  number,  the  sum  of  all  the  odd  num 
bers  iu  the  first  series,  up  to  and  including  the  one 
under  which  the  sum  is  placed  ;  and  the  same  with 
respect  to  the  even  numbers.  Then,  the  second  series 
of  figures  may  be  used  in  precisely  the  same  manner 
as  that  explained  with  reference  to  Fig.  12,  to  deter 
mine  the  weight  sustained  by,  and  the  maximum  stress 
produced  upon,  each  diagonal  and  vertical,  by  equal 
weights  upon  all  or  any  of  the  nodes  of  either  chord. 

For  example;  supposing  the  truss  to  have  tension 
diagonals  and  thrust  verticals;  take  the  diagonal  hav- 
its  lower  end  under  5  (upper  series),  and  its  upper  end 
under  7.  This  diagonal  may  be  represented  by  5/7, 
while  5\7  may  indicate  its  antagonist,  and  so  of  other 
diagonals.  Then,  as  we  see  9  (the  sum  of  1  +  3  +  5),  in 
the  second  series,  over  the  lower  end  of  5/7,  and,  as  the 
diagram  represents  a  truss  of  16  panels,  we  know  that 
the  diagonal  in  question  is  liable  to  a  maximum 
weight  of  TV#,  =  9w".  This  amount  is  to  be  dimin 
ished,  of  course,  by  the  weight  due  from  weight  of 
structure  to  the  counter  diagonal. 

Again,  the  diagonal  9/11  sustains  as  amaximnm  from 
variable  load,  25w";  which  will  require  to  be  increased 
on  account  of  weight  of  structure,  since  the  latter,  in 
this  case,  acts  upon  the  main,  and  not  upon  the  counter 
diagonal,  as  in  case  of  5/7. 

Now,  to  obtain  the  effects  of  weight  of  structure  and 
uniform  load,  the  truss  having  even  panels,  we  place  J 
under  the  centre  node  of  the  lower  chord,  because 
half  of  the  weight  w',  which  is  supposed  to  be  concen 
trated  at  that  point,  tends  to  act  on  each  of  the  dia 
gonals  rising  from  that  point. 


DOUBLE  CANCELATED  TRUSSES. 


83 


oo 


At  the  next  node  from  the 
centre,  each  way,  the  figure  1 
is  set,  because,  of  the  weights 
(M/), concentrated  at  those  points, 
each  bears  upon  its  nearest  abut 
ment  (the  truss  being  uniformly 
loaded),  through  the  diagonals 
running  upward  and  outward 
from  those  points.  If  this  be 
not  so,  each  must  transmit  a  part 
of  its  amount  past  the  centre, 
through  the  antagonistic  dia 
gonals  7/9  and  7\9,  which  is 
contrary  to  statical  law. 

Then  we  put  1J,  2J,  3J,  etc., 
under  alternate  nodes  from  the 
centre,  and  1,  2,  8,  etc.,  under 
alternates  beginning  at  the  first 
on  each  side  of  the  centre ;  as 
shown  in  diagram  Fig.  18. 

These  figures  form  the  co 
efficients  of  w',  to  indicate  the 
weights  acting,  or  tending  to 
act,  upon  the  diagonals  running 
upward  and  outward  from  these 
numbers  respectively,  arising 
from  weight  of  structure,  and 
also,  the  co-efficients  for  (iv+wf), 
to  express  the  load  tending  to 
act  on  diagonals,  arising  from 
both  superstructure  and  mova 
ble  weight,  when  the  truss  is 
fully  loaded.  For  illustration  ; 


34  BRIDGE  BUILDIXG. 

the  diagonal  5/7  we  have  seen  to  be  liable  to  a 
maximum  stress  of  §w"  from  variable  load,  and,  as  we 
have  the  figure  1  at  the  foot  of  5\7,  it  shows  that 
the  weight  due  to  the  latter  on  account  of  structure 
is  IM?',  which  must  be  subtracted  from  §w"  to  obtain 
the  actual  maximum  to  which  5/7  is  liable ;  which 
is  Qu)"—.w'. 

If  w'  be  equal  to  or  greater  than  9w",  then  5/7  ia 
subject  to  no  action,  and  may  be  dispensed  with.  As 
to  the  advantage  of  introducing  counter  diagonals, 
merely  for  the  purpose  of  stiffening  the  truss,  the  results 
of  my  investigations  will  be  given  in  a  subsequent  part 
of  this  work. 

The  maximum  weight  sustained  by  any  thrust  up 
right,  is  manifestly  equal  to  the  greatest  weight  borne 
by  either  diagonal  connected  with  it  at  the  upper  end, 
since  any  weight  borne  by  3/5,  for  instance,  being 
transferred  to  the  antagonist  of  5\7,  thereby  dimin 
ishes  by  a  like  amount,  the  maximum  action  of  the 
latter.  Whence  the  upright  at  5,  can  receive  no  more 
load  from  the  two  diagonals,  than  the  maximum  load  of 
one,  and  this  relation  holds  in  general. 

The  reason  of  adding  alternate  figures  to  form  the 
second  series  over  the  diagram,  will  be  obvious,  when 
it  is  observed  that  there  are  two  independent  systems 
of  uprights  and  diagonals ;  one  of  which  includes  the 
uprights  under  even  numbers  in  the  upper  series,  and 
the  diagonals  connecting  therewith,  and  the  other,  the 
remaining  uprights  and  diagonals.  Now  weight  applied 
at  the  nodes  of  either  of  these  systems,  can  only  act  upon 
members  of  that  same  system  ;  that  is,  weight  applied 
at  nodes  indicated  by  even  numbers  in  the  upper  series 
can  only  act  upon  the  first  above  named  system  of  up 
rights  and  diagonals,  and  vice  versa. 


DOUBLE  CANCELATED  TRUSSES.  85 

The  main  end  braces  are  acted  upon  by  both  sys 
tems;  so  that  to  obtain  the  weight  sustained  by  them, 
we  must  add  the  numbers  56  and  64  (and  correspond 
ing  numbers  in  other  cases),  making  in  this  case  12(W 
equal  to  7Jw. 

The  uprights  under  1  and  15,  sustain  each  a  tension 
equal  to  w,  for  variable  load,  and  to  w+w',  for  weight 
of  variable  load  and  superstructure  together ;  which 
obviously  gives  their  greatest  strain. 

Having  thus  determined  the  greatest  weights  to  which 
the  several  verticals  and  diagonal  members  are  liable, 
we  proceed  as  in  former  cases,  to  multiply  those 
weights  by  lengths  of  diagonals,  and  divide  the  pro 
ducts  by  lengths  of  verticals,  to  obtain  the  stresses  of 
diagonals ;  remembering  to  take  into  account  the  dif 
ference  in  length  between  those  having  a  horizontal 
reach  of  only  one  panel,  at  and  near  the  ends  of  the 
truss,  and  those  that  reach  across  two  panels. 

The  mode  of  estimating  the  stresses  upon  the  differ 
ent  portions  of  the  chords,  depending  upon  the  hori 
zontal  action  of  diagonals,  has  been  sufficiently  ex 
plained.  It  is  only  necessary  to  observe  that  the  end 
braces  produce  compression  upon  the  upper,  and  ten 
sion  upon  the  lower  chord,  through  their  whole  lengths, 
equal  to  £  (io+w'\  multiplied  by  the  number  of  nodes 
of  the  lower  chord,  and  that  product  multiplied  by  - . 
and  that  each  pair  of  intermediate  diagonals  analo 
gously  situated  with  respect  to  the  ends  of  the  truss, 
whether  acting  by  thrust  or  tension,  produce  tension 
and  thrust  in  like  manner,  upon  the  portions  of  the 
lower  and  upper  chords,  between  their  points  of  con 
nection  with  the  chords.  Thus  is  generated  a  progres 
sive  and  determinate  increase  of  action  upon  succeeding 


86  BRIDGE  BUILDING. 

portions  of  the  chords  from  the  ends  to.  the  centre  of 
the  truss. 

In  the  case  of  a  deck  bridge,  the  weights  sustained 
by  thrust  uprights,  are  respectively  indicated  by  the 
figures  over  the  diagram  on  the  right  hand  half  of  the 
truss,  prefixed  to  w",  for  movable  load,  and  the  figures 
under  the  diagram  prefixed  to  w',  for  weight  of  struc 
ture,  being  the  same  weight  which  gives  the  maximum 
stress  to  the  diagonal  running  upward  and  outward 
from  the  foot  of  the  upright.  Tension  verticals  at  the 
ends  sustain  no  weight. 


TRUSSES  WITHOUT  VERTICALS. 

It  will  be  seen  upon  a  general  view  of  the  action  of 
the  different  parts  of  a  truss  with  parallel  chords,  that 
the  diagonals  (and  verticals  when  used),  form  media 
through  which  weight  acting  upon  the  truss,  is  reflected 
back  and  forth  between  the  upper  and  lower  chords, 
until  it  comes  finally  to  bear  upon  the  abutment. 

A  weight  applied  at  one  of  the  nodes  of  the  lower 
chord,  of  course,  cannot  be  sustained  by  the  tension 
of  that  chord,  which  acts  only  in  horizontal  directions ; 
but  is  suspended  by  a  tension  piece,  whether  oblique 
or  vertical,  from  a  node  in  the  upper  chord.  But  the 
upper  chord  acting  also  horizontally,  cannot  sustain  the 
weight.  Consequently,  a  thrust  member,  either  oblique 
or  vertical,  must  meet  the  force  at  that  point,  to  prevent 
the  weight  from  pulling  down  the  upper  chord,  and 
destroying  the  structure. 

Hence,  we  see,  that  in  all  the  cases  we  have  consid 
ered,  of  trusses  with  parallel  chords,  the  weight,  whe 
ther  applied  at  the  upper  or  lower  chord,  acts  alter- 


TRUSSES  WITHOUT  VERTICALS.  87 

nately  upon  thrust  and  tension  pieces,  extending 
directly  or  obliquely  from  chord  to  chord. 

With  reference  to  Fig.  18,  we  have  regarded  the 
weight  as  transferred  from  tension  diagonals  to  thrust 
verticals,  and  the  contrary.  But  if  we  conceive  the 
verticals  to  be  removed,  except  the  endmost,  we  have 
only  to  insert  a  thrust  brace  from  the  abutment  to  the 
second  node  (or  the  first  from  the  angle),  of  the  upper 
chord,  and  to  so  form  and  connect  the  other  diagonals 
as  to  enable  them  to  act  by  either  tension  of  thrust, 
and  we  have  a  truss  capable  of  sustaining  weights  applied 
at  all,  or  any  of  the  nodes  of  the  upper  and  lower 
chords,  in  the  same  manner  as  the  truss  with  verticals, 
represented  in  Fig.  18.  In  this  condition,  the  truss 
will  act  upon  the  principles  discussed  with  reference  to 
Fig.  18.  For  this  modification  of  the  truss,  see  Fig.  19. 

To  estimate  the  strains  upon  the  several  parts  of 
such  a  truss,  due  to  weights  w,  w,  etc.,  at  the  nodes  of 
the  lower  chord  ;  we  may  place  the  figures  1,  2,  3,  etc., 
over  the  nodes  of  the  upper  chord,  as  was  done  in  the 
case  of  Fig.  18.  But,  instead  of  adding  alternate  fig 
ures  to  form  the  second  series,  to  be  used  as  co-eili- 
cients  of  w" ,  for  expressing  the  weights  sustained  by 
diagonals,  we  add  every  fourth  figure;  because  it  is 
only  the  weights  at  every  fourth  node,  that  act  upon 
the  same  set  of  diagonals. 

For  instance  ;  the  weights  at  1,  5,  9  and  13,  act  upon 
their  peculiar  set  of  8  pieces  (excluding  the  end  braces, 
but  including  the  tension  vertical  at  1),  a»nd  none  of  the 
weights  at  the  other  nodes  have  any  action  upon  those 
pieces  ;  as  is  made  obvious  by  an  inspection  of  Fig.  19. 

Again,  the  weight  at  2,  6,  10  and  14,  have  their  pe 
culiar  and  independent  set ;  and  so  of  those  at  3,  7,  11 
and  15,  and  those  at  4,  8  and  12.  Therefore,  in  form- 


88 


BRIDGE  BUILDING. 


0  00  00 

1—1    1— I 


C510O 


*>  o  '- 


ing  our  second  series  of  num 
bers,  we  place  under  each  figure 
of  the  first  series,  the  sum  of 
that  figure,  added  to  every  4th 
figure  preceding;  that  is,  under 
12,  place  the  sum  of  12,  8  and  4 
••=  24.  %  Under  5,  the  sum  of  5-f 
1  =6.  The  four  first  figures, 
having  no  4th  preceding  figures, 
are  simply  transferred,  without 
addition  or  alteration. 

These  numbers  in  the  second 
series,  are  the  co-efficients  of  w" 
(—w  divided  by  the  number  of 
panels  in  the  truss,  being  16  in 
this  case),  to  express  the  greatest 
weights  acting  by  tension  on 
each  diagonal  having  its  lower 

o  o 

end  under  the  number  used,  and 
the  upper  end  under  a  higher 
number.  Also  the  weight  act 
ing  by  thrust  upon  the  diagonal 
meeting  the  former  at  the  upper 
chord.  The  last,  or  highest 
number,  determines  the  weight 
sustained  by  the  tension  vertical 
under  the  number,  the  vertical 
being  a  member  of  one  of  the 
four  sets  ot  alternate  thrust  and 
tension  pieces  connecting  the 
two  chords. 

A  third  series  of  figures 
formed  by  reversing  the  order 
of  the  second — placing  the  low- 


TRUSSES  WITHOUT  VERTICALS.  89 

est  number  of  the  third  under  the  highest  of  the  se 
cond  series,  and  vice  versa,  prefixed  as  before  to  w" ', 
will  show  the  weights  sustained  by  thrust  and  tension 
of  diagonals  in  the  reversed  order;  i.  e.,  whereas  one 
series  shows  the  amount  of  tension  a  particular  diago 
nal  is  liable  to,  the  reversed  series  shows  the  thrust 
the  same  piece  must  exert  in  a  different  condition  of 
the  load. 

Thus  we  ascertain,  as  in  the  case  of  truss  Fig.  13 
[XLV],  that  nearly  all  of  the  diagonals  are  exposed  to  two 
kinds 'of  action,  thrust  and  tension  ;  and  it  is  only  the 
preponderance  of  the  larger  over  the  smaller  of  these 
forces,  which  has  place  when  the  truss  is  fully  loaded, 
and  it  is  only  this  preponderance  which  is  to  be  used 
as  co-efficient  to  (w  +  w1)  in  estimating  the  stresses  upon 
the  different  portions  of  the  chords,  and  as  co-efficient 
to  ?/;',  in  modifying  the  effects  of  the  variable  load  upon 
diagonals,  as  aftected  by  weight  of  structure.  But  it  is 
to  be  remembered  that  the  numbers  over  the  diagram 
are  to  be  divided  by  the  number  of  panels,  before  being 
used  before  w  and  w',  in  the  expression  of  stresses  of 
members.  Thus,  we  have,  as  the  effect  of  variable 
load  upon  the  diagonal  2/4  ...,  2w" (=^w),  as  the 

1  Q 

greatest  weight  acting  by  tension,  and  ~^w9  the  great 
est  acting  by  thrust.  Hence  the  weight  upon  this 

-|  Q f) 

piece,  due  to  weight  of  structure,  is  (-- -~-)wf9—w'9  and  it 
produces  thrust  or  compression,  because  the  thrust 
tendency  is  the  greater.  This  weight  (w'},  added  to 
-8w,  the  greatest  effect  of  variable  load  shows  the  maxi 
mum  weight  which  can  act  by  thrust  upon  that  diago- 

"1  ft 

nal,  to  be  -^w+w'.  We  have,  also,  for  the  greatest 
weight  acting  by  tension  as  modified  by  weight  of  struc- 

12 


90  BRIDGE  BUILDING. 

ture,  pit1 — iv'j  which  is  a  negative  quantity  when  w  is 
less  than  8w',  as  will  usually  be  the  case  in  practice ; 
consequently  that  diagonal  can  seldom  or  never  be  ex 
posed  to  the  force  of  tension. 

Again  —.(w+w')-,  (h  and  v  representing  horizontal 
and  vertical  reaches  of  the  diagonal,  as  in  previous 
discussions),  is  the  amount  contributed  toward  the 
maximum  tension  of  the  lower  chord  by  the  diagonal 
in  question,  not  affecting,  of  course,  that  portion  of 
the  chord  outside  of  the  connection  therewith,  or  a 
like  portion  at  the  opposite  end. 

LYIII.  It  is  to  be  remembered  that  the  tension  or 
thrust  of  a  diagonal,  is  always  equal  to  the  weight  sus 
tained,  multiplied  by  the  length,  and  divided  by  the 
vertical  reach  of  the  diagonal. 

The  method  here  under  discussion  for  estimating 
stresses,  seems  to  need  no  further  illustration.  But 
the  question  as  to  decussation,  affects  the  case  of  Fig. 
19,  as  well  as  that  of  Fig.  13.  The  two  sets  of  dia 
gonals  which  meet  the  upper  and  lower  chords  in  the 
centre,  have  symmetrical  halves  on  each  side  of  the 
centre,  and  no  action  can  pass  the  centre  upon  either, 
when  they  are  uniformly  loaded  ;  whereas,  the  two  seta 
to  which  7/9  and  7\9  belong,  have  the  half  of  one 
on  either  side  of  the  centre,  a  counter  part  to  the  half 
of  the  other  set  on  the  opposite  side  ;  and  the  diagonals 
7/9  and  7\9,  will  act  or  not,  according  as  their  op 
posite  points  of  connection  with  upper  and  lower  chords, 
are  carried  farther  apart,  or  the  contrary.  JSTow,  as 
the  points  9  and  7,  upper  chord,  are  depressed  by  the 
change  in  one  vertical  and  3  diagonals,  while  the  op 
posite  points  at  the  lower  chord  are  depressed  by  the 


TRUSSES  WITHOUT  VERTICALS.  91 

change  in  3  diagonals  only,  we  might  naturally  expect 
to  find  greater  depression  iu  the  upper  than  the  lower 
points;  though  this  does  not  follow  as  a  matter  of  .ne 
cessity,  since  the  less  number  of  members,  by  being 
more  nearly  under  a  maximum  stress,  might  give 
greater  depression  than  the  greater  number,  under  less 
stress,  as  compared  with  their  maximum.  Now,  the 
vertical  at  1,  being  under  maximum  weight,  gives  de 
pression  =  E  ;  (adopting  the  notation  used  with  refer 
ence  to  Fig.  13  [XLIX.]).  The  two  diagonals  1/3  and 
3\5  being  under  f  J  maximum,  give  depression  equal 
toff  x4E(making/i=*;=l),  =  3.81E;  while  the  diagonal 
5/7,  under  T4^  maximum,  gives  depression  =  0.4  x2E, 
=  0.8E,  making  a  total  depression  of  point  7,  upper 
chord,  =  5.6 IE.  Again,  the  diagonal  1\3,  under  maxi 
mum  stress,  gives  depression  =  2E,  while  3/5  and 
5\7,  under  j  f  rnaxm  u  m  stress,  give  depression  =  -J  X 
4E,  =  3.2E,  making  a  total  for  the  point  7,  lower  chord, 
equal  to  5.2E,  which  is  less  by  0.41E,  than  the  depression 
of  the  opposite  point  in  the  upper  chord,  whereas  it 
should  be  greater  by  0.8E,  in  order  to  give  to  7\9  and 
7/9,  the  tension  assigned  to  them  by  the  decussation 
theory. 

But  we  must  not  conclude  from  this  fact,  that  there 
is  no  decussation  in  this  case.  For,  if  we  assume  that 
7\9  is  inactive  under  the  full  load,  it  follows  that  5/7 
is  also  inactive,  and  that  l/3-|-3\5  sustain  only  Jf 
maximum  stress,  producing  f  }E,  =  3.05  E,  which  added 
to  IE  for  the  vertical  at  1,  makes  4.05  E,  =  depression  at 
point  7,  upper  chord  ;  while  the  3  diagonals  contribut 
ing  to  depression  of  the  opposite  point  in  lower  chord, 
are  under  maximum  stress,  producing  depression  =  6  E. 
Hence,  we  see,  that  upon  this  hypothesis,  the  distance 
between  these  two  points,  measuring  the  vertical  reach 


92  BRIDGE  BUILDING. 

of  the  diagonal,  is  increased  by  (6 — 4.05)E  =  1.95E. 
This  can  not  be,  without  producing  tension  upon  dia 
gonals  7\9  and  7/9.  Since  then  these  members  can 
not  be  entirely  without  action,  and  as  previously  shown, 
they  can  not  have  as  much  action  as  the  decussation 
theory  assigns  to  them,  it  follows,  in  this  case,  that  they 
must  act,  but  with  less  intensity  than  the  theory  as 
signs  them. 

In  this  case,  as  well  as  in  that  of  Fig.  13,  the  result 
would  be  changed  somewhat,  by  taking  into  the  cal 
culation  the  weight  of  structure,  which  would  change 
to  a  small  extent,  the  relation  between  the  maximum 
stresses  of  diagonals,  and  the  stresses  they  sustain  un 
der  a  full  load.  .For  the  stress  due  to  weight  of  struct 
ure,  is  constant,  and  that  due  to  variable  load,  is  greater, 
upon  most  of  the  diagonals,  under  certain  conditions 
of  a  partial,  than  under  a  full  load.  Hence,  while 
5\7  sustains  (under  full  load),  only  {§  maximum  upon 
that  part  of  the  material  provided  for  variable  load,  it 
sustains  a  full  maximum  upon  the  part  provided  to 
sustain  weight  of  structure.  It  is  easy  enough  to  take 
these  things  all  into  account,  in  estimating  the  amount 
of  decussation  in  special  cases.  Still,  it  is  doubtful 
whether  any  better  practical  rule  can  be  adopted,  than 
the  one  previously  given,  [XLVIII]  ;  namely,  to  estimate 
stresses  upon  both  hypotheses,  and  take  the  highest 
estimate  for  each  part. 

DECUSSATION  IN  TRUSSES  WITH  VERTICALS. 
LIX.  In  trusses  of  this  class  with  odd  panels,  and 
diagonals  crossing  two  panels,  as  in  Fig.  20,  it  will  be 
seen,  on  subjecting  them  to  analysis,  such  as  was  ex 
plained  with  reference  to  Fig.  18  [xvi],  that,  while  in 
trusses  of  even  panels,  the  figures  in  the  second  line 


DECUSSATION,  ETC. 


93 


over  the  diagram,  indicate  the  maximum  stresses  of 
diagonals,  and  those  under  the  diagram,  the  stresses 
under  uniform  load  (which  are  generally  less  than  the 
maximum  under  partial  loads),  in  case  of  the  truss  with 
odd  panels,  the  bottom  figures  show,  for  certain  dia 
gonals,  greater  stresses  for  the  full,  than  the  upper 
figures  give  as  the  maximum  for  partial  loads.  Thus, 
in  Fig.  20,  the  number  16  over  m,  indicates  16*0" 
(=ijj6 z0),  as  the  maximum  weight  for  #,  while  the  fig 
ure  2  under  the  point  z,  indicates  that  il  sustains  2i0  (  = 
18i0"),  under  the  full  load.  It  should  be  remarked  here, 
that  the  figure  1  under  the  first  two  nodes  on  either  side 
of  the  centre,  and  the  figure  2  under  the  next,  are  thus 


2        2 


FIG.  20. 

45678 
6        9       12       16       20 


q         p 


XKXxx 
xxRx 


abcdefgijk 
211112 

placed  upon  the  assumption  that  all  the  weight  on 
either  side  of  the  centre,  is  made  to  act  on  its  nearest 
abutment.  This  would  necessarily  be  so,  if  en  andfq 
were  removed  or  relaxed.  But,  with  those  members 
in  place,  and  properly  adjusted,  there  may  be  a  decus- 
sation  of  forces  through  them,  whereby  a  portion  of 
the  weights  at  e  and/,  may  be  made  to  bear  upon  the 
more  remote  abutments.  Now,  as  the  maximum  on 
en  is  6w"  and  that  of  its  antagonist  only  4w",  the  latter 
is  not  sufficient  to  neutralize  the  former  entirely,  but 
leaves  a  balance  of  2wff  which  may  be  transmitted 
through  en  to  gl,  as  an  offset  for  a  like  amount  trans- 


94  BRIDGE  BUILDING. 

mitted  through/^  to  ds.  If  this  be  so,  then  fm  and  er 
do  not  sustain  the  full  weight  of  liv,  but  only  W9 
which,  being  transmitted  to  U9  makes,  with  the  weight 
w  (=9w;"),  applied  directly  at  i,  16w",  as  indicated  by 
the  figures  over  the  diagram,  instead  of  2w  (=  ISic"), 
as  the  figure  2  under  the  point  i  would  indicate. 

Now,  whether  the  two  diagonals  en  and/<?,  being  ap 
parently,  in  a  state  of  partial  antagonism,  do  in  whole 
or  in  part  neutralize  the  tendency  of  each  other  to 
transmit  weight  past  the  centre  each  way  under  a  uni 
form  load  of  the  truss,  is  not  quite  obvious,  and  it  may 
be  proper  to  estimate  stresses  under  both  hypotheses, 
and  take  the  highest  estimate  for  each  part  of  the 
truss. 

It  will  be  seen  that  it  and  cs  are  the  only  diagonals 
in  Fig.  20,  which  show  greater  stress  with  a  full  than 
a  partial  load,  upon  the  non-decussation  hypothesis. 
But  all  the  diagonals  undergo  different  stresses,  with 
the  uniform  load,  as  viewed  under  the  different  theo- 
riSs,  and  consequently,  their  effects  upon  the  chords 
are  different.  The  end  brace  as,  sustains  4  (w+w')  = 
4W  substituting  W  for  w-rwf),  under  either  theory, 
and  the  tension  of  ac  equals  4w  (making  A  =  #6,  and 
v  =  bs).  cs  sustains  2~VV,  or  y  TV",  whence  cd  sustains 
either  6W^  or  5JW*.  Again,  ds  sustains  W,  or  IfW, 
the  former  without,  and  the  latter  with  decussation. 
This  diagonal  having  a  horizontal  reach  of  2A,  adds 
2W-  or  2JW-  to  tension  of  chord,  making  8W*,  or 

8f  W  ,  as  the  tension  of  de.  For  er,  we  have  W  with 
out  decussation,  making  a  tension  of  10W-  for  ef; 
while  with  decussation,  er  sustains  J  W,  from  which  we 
subtract  f  W",  for  opposite  action  of  en,  leaving  |W 


DECUSSATION,  ETC.  95 


giving  horizontal  pull  =1J  W    to   be  added  to   S 

making   9jW-  =»  tension  of  ef. 

Upon  the  non-decussation  hypothesis,  5  r  and  m  l>  of 
the  upper  chord  sustain  thrust  equal  to  8W^,  and  the 

remainder  of  the  chord,  10W-.  By  the  other  hypothe 
sis,  sr  and  ml  sustain  8f  W  -,  rq  and  nm  sustain  9J 
W  *,  and  the  other  3  sections,  lOf  W^  ' 

LX.  "We  may  derive  some  more  light  upon  this  sub 
ject,  by  considering  the  conditions  resulting  from  the 
elasticity  of  materials.  Supposing  the  upper  and  lower 
chords  to  be  so  proportioned  as  to  be  uniformly  con 
tracted  or  extended  under  a  uniform  load  of  the  truss, 
this  does%not  require  or  imply  any  appreciable  differ 
ence  in  lengths  of  diagonals.  But  the  stress  upon 
chords  being  produced  by  the  action  of  diagonals,  the 
latter,  when,  as  here  supposed,  acting  by  tension,  neces 
sarily  undergo  extension,  by  which  means,  the  panels 
(except  the  centre  one),  are  changed  from  their  original 
form  of  rectangles,  to  that  of  oblique  trapezoids.  For 
instance,  the  figure  gj.ln  becomes  longer  diagonally 
from  g  to  £,  than  from  n  toj,  whence  the  point  g  falls 
lower  than  it  would  do,  if  the  diagonal  suffered  no 
change. 

Suppose  then  the  truss  to  be  fully  loaded,  and  the 
diagonals  il,  gl  and/m,  to  be  each  exposed  to  the  same 
stress  to  the  square  inch  of  cross-section.  In  that  case, 
il  and  gl  suffer  extension  proportionally  to  their  respec 
tive  lengths,  thereby  causing  depression  of  the  points 
i  and  g  respectively  as  the  squares  of  those  lengths. 
[See  note  in  section  XLIX.]  Hence,  the  point  g  is  de- 


96  BRIDGE  BUILDING. 

pressed  more  than  the  point  j,  by  the  extension  of  dia 
gonals,  by  as  much  as  the  square  of  gl  exceeds  the 
square  of  il,  or  as  8  to  5 ;  assuming  diagonals  to  incline 
at  45°.  The  panel  gm,  must  therefore  be  oblique,  and 
the  distance  gm,  greater  than  ni.  Again,  the  point/ 
suffering  the  same  depression  from  the  extension  of/w, 
as  the  pointy  suffers  from  that  of^,  and  a  still  further 
depression  from  the  compression  of  mi,  and  the  exten 
sion  of  il,  it  fo.llows  that  the  panel  fn  must  also  be  ob 
lique,  and  the  distance /ft,  greater  than  the  distance  og. 

Now,  the  obliquity  of  both  of  the  panels  gm  and//i, 
manifestly  contributes  to  the  excess  of  distance  fm, 
over  01.  On  the  contrary,  the  centre  panel  eo  has  no 
obliquity  due  to  extension  of  diagonals,  or  compression 
of  uprights;  since  there  is  no  cause  for  obliquity  in 
one  direction,  more  than  the  other.  It  seems  to  follow 
that  en,  crossing  one  oblique  panel,  must  undergo  ex 
tension;  but  not  so  much  as //n, which  crosses  two. 

Now, ///i  and  en  being  equal  in  length,  the  weight 
sustained  by  each,  is  manifestly  as  the  cross-section 
and  extension  combined  ;  and  as  the  former,///?.,  should 
be  the  larger  in  the  ratio  of  9  to  6,  or  as  their  maxi 
mum  stresses ;  if  we  allow  their  extensions  to  be  as 
2  to  1,  the  greater  for/w,  the  relative  weights  sustained 
would  be  as  18  to  6,  or  as  6  to  2.  Our  decussation 
theory  gave  their  relative  stresses  as  Iw"  to  2w/f.  This 
is  not  a  wide  discrepancy,  seeing  that  the  above  com 
putation  is  based  in  part  upon  a  mere  approximate 
data.  -w 

We  may  conclude  then,  that  in  cases  like  the  one 
under  consideration,  decussation  does  actually  take 
place.  Still  it  obviously  depends  upon  conditions  which 
are  not  of  the  most  determinate  character.  For,  if  en 
and/?,  be  relaxed  or  removed,  under  a  full  load  of  the 


DECK  BRIDGES.  97 

truss,  dccussation  can  not  take  place,  for  the  same  ob 
liquity  of  the  two  panels  next  to  the  centre  one,  which 
produces  the  tendency  toward  tension  of  en  and/*?,  O11 
the  contrary,  tends  to  relax  do  and  gp,  through  which 
latter  alone  decussation  could  take  place,  in  the  absence 
of  the  former. 

On  the  other  hand,  if  en  audfq  be  sufficiently  strong, 
they  may  be  strained  to  such  a  pitch  as  to  bear  all  the 
weights  ate  and/,  andleave/m  and  er  entirely  inactive. 
Hence,  there  is  an  uncertainty  as  to  the  action  of  these 
diagonals,  which  may  be  best  obviated  by  estimating 
stresses  upon  both  theories,  and  taking  the  highest  es 
timates  ;  as  recommended  with  reference  to  trusses 
without  verticals,  and  as  previously  suggested  with 
reference  to  the  case  in  hand. 

In  view  of  preceding  facts  and  principles,  it  may  be 
advisable  to  avoid  the  odd  panel  in  trusses  with  verti 
cals,  when  practicable  without  incurring  more  import 
ant  disadvantages  in  other  respects. 


DECK  BRIDGES. 

LXL  Are  those  having  the  movable  load  applied  at 
the  nodes  of  the  upper,  instead  of  the  lower  chord,  as 
generally  assumed  in  preceding  analyses. 

It  will  readily  be  seen,  on  a  brief  contemplation  of 
Figures  12  and  13,  for  instance,  that  weights  applied 
at  the  upper  chord,  act  directly  upon  compression 
members,  either  erect  or  oblique,  as  the  case  may  be  ; 
and  are  thence  transferred  to  tension  members  at  the 
lower  chord ;  according  to  the  general  principle,  that 
weight  applied  at  the  upper  end  of  a  member,  always 
acts  by  compression,  and  that  which  is  applied  at  the 
lower  end,  by  tension. 
13 


98  BRIDGE  BUILDING. 

In  the  case  of  truss  Fig.  12,  the  action  of  tension  di 
agonals  is  precisely  the  same,  whether  the  weight  be 
applied  at  the  upper  or  lower  chord.  But  the  compres 
sion  verticals,  in  the  deck  bridge,  sustain  as  their  maxi 
mum,  the  weights  indicated  by  the  figures  immediately 
above  them  respectively,  from  the  centre  toward  the 
right  hand ;  and  these  weights,  of  course,  are  equal  to 
those  acting  upon  the  diagonals  respectively  meeting 
the  verticals  at  the  lower  chord;  and  consequently, 
greater  than  when  the  weight  is  applied  at  the  lower 
chord.  For  illustration,  in  Fig.  12,  as  the  truss  of  a 
deck  bridge,  the  vertical  fk  sustains  15w;",  the  same  as 
jjf,  whereas,  in  the  case  of  a  "  Through  bridge"  (with 
load  applied  at  the  lower  chord),  fk  sustains  only  IQiv" 
communicated  to  it  through  ek. 

In  the  deck  bridge  also,  the  tension  verticals  bo  and 
jg  are  essentially  inactive,  merely  sustaining  a  small 
portion  of  the  lower  chord.  The  chords  suffers  the 
same  stress  in  both  through,  and  deck  bridges. 

LXII.  Load  applied  at  the  upper  chord  of  truss  Fig. 
13,  acts  by  thrust  directly  upon  the  diagonals  meeting 
at  the  upper  chord,  and  the  maximum  weight  (from 
movable  load),  sustained  by  diagonals  meeting  at  one 
of  the  upper  nodes,  are  indicated  by  the  two  figures 
immediately  over  the  node  ;  the  larger  figure  referring 
to  the  diagonal  running  toward  the  nearer  abutment  ; 
e.  g.,  the  numbers  4  and  6  over  the  point  m,  signify 
ftw"  =  greatest  weight  borne  by  me,  and  4w"  —  the 
greatest  borne  by  me. 

It  is  obvious  also,  that  the  maximum  thrust  of  any 
diagonal,  equals  the  maximum  tension  of  the  diagonal 
meeting  the  former  at  the  lower  chord  ;  that  is,  maxi 
mum  thrust  of  me,  is  equal  to  6w"— ,  =  maximum  ten- 


DECK  BRIDGES.  99 

sion  of  co.  The  maximum  thrust  of  bn  being  equal  to 
9i0"--,  the  maximum  tension  of  bo,  equals  §w"  .  Tins  is  an 
extra  weight  thrown  upon  the  point  o,  in  consequence  of 
the  vertical  bo,  being  turned  out  of  its  regular  direction 
of  a  diagonal  in  the  position  of  bp*  in  order  to  throw 
its  load  upon  oa,  whereby  op  and  pa  are  rendered  un 
necessary.  The  weight  borne  by  oa,  therefore,  instead 
of  being  12^;",  as  indicated  by  the  figure  12  at  o,  is 


The  figure  1  over  o,  denotes  the  tendency  of  \w"  to 
act  upon  oc,  by  thrust,  by  which  tendency  the  tension 
of  oc,  under  a  full  load  of  the  truss,  is  reduced 
to  5tf"£. 

LXIII.  If  Fig.  12  be  assumed  to  represent  a  truss 
with  tension  verticals  and  thrust  diagonals,  the  figures 
over  the  upper  nodes,  prefixed  to  wn  indicate  the 
weights  tending  to  act  by  compression  upon  the  dia 
gonals  descending  toward  the  right  from  the  nodes 
respectively  ;  which  weight  is  transferred  to  the  verti 
cal  meeting  the  diagonal  at  the  lower  chord.  This 
constitutes  the  maximum  load  of  the  vertical,  in  case 
of  a  deck  bridge.  Otherwise,  the  maximum  stress  of 
verticals  is  shown  by  the  figures  immediately  over 

FIG.  13A. 

v  o  n  m  I  k  j 


a  b  c  d  e  f  //  i 

*  The  point  p,  not  seen  in  Fig.  13,  is  assumed  to  be  at  the  intersec 
tion  of  a  vertical  line  through  the  point  a,  with  the  upper  chord- 
produced.  The  arrangement  above  alluded  to,  gives  the  truss  a  reclan- 
gular,  instead  of  a  trapezoidal  form  of  outline,  which  involves  no  more 
action  upon  material,  'though  it  increases  the  number  of  members  in 
the  truss.  [See  Fig.  13A.] 


100  JLJRIDGE  BLILDING. 

• 
them,  prefixed  to  10",  provided,  that  in  this  case,  the 

maximum  stress  of  a  vertical  can  never  be  less  than  w. 
=  the  weight  applied  immediately  at  its  lower  end. 

RATIO  OF  LENGTH  TO  DEPTH  OF  TRUSS. 

LXIV.  Having  explained  and  illustrated,  it  is  hoped 
intelligibly,  methods  by  which  may  be  computed  the 
stresses  of  the  various  parts  composing  most  of  the 
combinations  of  members  capable  of  being  used  in 
bridge  trusses,  with  a  view  to  giving  to  each  part  its 
due  proportions,  it  may  be  proper  to  give  attention  to 
the  general  proportions  of  trusses,  and  such  other  con 
siderations  as  may  affect  the  efiicient,  and  economical 
application  of  materials  in  bridge  construction. 

The  ratio  of  length  to  depth  of  truss  is  susceptible 
very  great  range,  and  it  is  obvious  that  some  certain 
medium,  in  this  respect,  will  generally  give  more  ad 
vantageous  results,  than  any  considerable  deviation 
toward  either  extreme.  For,  it  will  be  observed,  that 
in  the  expressions  we  have  derived  for  the  amount  of 
action  open  chords,  -  appears  as  a  factor ;  v  represent 
ing  the  depth  of  truss,  between  centres  of  chords. 
Hence,  the  smaller  the  value  of  v,  the  greater  the 
stresses  of  chords,  so  that  when  v=0,  these  stresses 
become  infinite,  and  the  chords  require  an  infinite 
amount  of  material ;  in  other  words,  the  case  is  im 
possible.  On  the  other  hand,  if  v  be  infinitely  great, 
though  the  stress  of  chords  be  reduced  to  nothing,  the 
verticals  and  diagonals  being  infinitely  long,  and  sus 
taining  a  definite  weight,  also  require  an  infinite 
amount  of  material. 

Now,   between   these  two  impracticable  extremes 
where  shall  we  look  for  the  most  advantageous  ratio  ! 


LENGTH  TO  DEPTH  OP  TRUSS.  101 

It  can  not  be  the  arithmetical  mean,  for  there  is  no 
such  mean  between  v  =  0,  and  v  —  infinity.  Un 
doubtedly,  we  shall  be  unable  to  do  more  than  answer 
this  question  approximately;  and  that,  only  with  refer 
ence  to  specific  cases;  for  the  ratio  suitable  for  one 
length  of  span,  and  in  one  set  of  circumstances,  will 
often  be  found  quite  unsuitable  under  different  circum 
stances. 

WQ  have  seen  that  the  material  required  in  chords, 
is  in  general,  inversely  as  the  depth  of  truss,  or  as  -. 
Also,  that  the  material  for  verticals  and  diagonals,  in 
creases  with  increase  in  the  value  of  v  ;  though  not  h 
a  determinate  ratio.  But  assuming  the  latter  classes 
of  members,  including  the  main  end  braces  of  the  Trape 
zoidal  truss,  to  increase  in  the  ratio  at  which  v  in 
creases,  while  the  chords  diminish  at  the  same  rate, 
we  might  reasonably  assume,  that  the  minimum  amount 
of  action  upon  materials  would  occur  when  the  amount 
of  action  upon  chords  were*  just  equal  to  that  upon  all 
other  parts  of  the  truss. 

By  recurrence  to  the  analysis  of  truss  Fig.  12, 
[XLIII],  we  find  amount  of  action  upon  chords,  re 
presented  by  56-M,  and  that  upon  all  other  parts,  by 


22.570)  M.  Here,  h  is  equal  to  J  part  of  the 
length  of  truss,  while  v  is  variable  ;  and,  by  making 
these  two  co-efficients  of  M  equal,  and  deducing  thence 
the  value  of  v,  we  have  the  depth  of  a  7  panel  truss  in 
which  the  amount  of  action  upon  chords,  equals  that 
of  all  other  parts.  Thus,  putting  56-  =  16--  4-  22.57i', 

substracting  16-,  and  multiplying  by  v,  we  have  40A2  = 
22.57^  ;  whence  v  =  </(^L],  =1.34A  nearly.  This 
gives  length  to  depth  of  truss,  as  5.2  to  1. 


102  BRIDGE  BUILDING. 

Again,  referring  to  analysis  of  truss  Fig.  10,  we  find 
action  upon  chords  represented  by  20--M,  and  action 

upon  other  parts,  by  (  8-  -f  11.2y)  M.  To  make 
these  quantities  equal,  requires  that?;  =  1.03A,  and  that 
the  length  of  truss  be  equal  to  ^  times  its  depth,  or 
nearly  5  to  1. 

From  this  last  case,  we  may  infer  as  a  probability  > 
that  a  ratio  of  length  to  depth  as  5  to  1,  is  the  most 
economical  for  a  truss  of  5  panels,  other  things  the 
same.  We  know,  moreover* that  by  making  v  =  J^»  in 
the  same  truss,  we  double  the  amount  of  action  upon 
chords  —  making  it  equal  to  the  aggregate  upon  all 
parts  with  the  ratio  of  5  to  1,  while  the  action,  and 
consequently,  the  material  of  the  other  parts  is  probably 
seduced  one-half.  Hence,  a  ratio  of  length  to  depth 
as  10  to  1,  probably  increases  the  aggregate  amount  of 
action  by  some  25  per  cent,  over  what  takes  place  with 
a  ratio  of  5  to  1.  We  may  therefore  unhesitatingly 
conclude,  that  whether  the  ratio  of  5  to  1  be  too  small 
or  not,  the  ratio  of  10  to  1  is  much  too  large. 

Referring  again  to  the  7  panel  truss,  it  appears  above, 
that  a  ratio  of  5.2  to  1  indicates  the  same  amount  of 
action  upon  chords,  as  on  all  other  parts.  But  we  can 
not  with  certainty  infer  that  the  absolute  amount  of  action 
upon  the  truss,  is  less  with  v=1.34/*,  than  with  v=h ; 
in  which  case  length  is  to  depth  a,s  7  to  1.  In  fact,  if 
we  estimate  the  absolute  amount  of  action,  assuming 
these  two  values  off  successively,  we  shall  find  no  es 
sential  difference  in  the  results.  Hence,  if  other  con 
ditions  were  the  same  in  both  cases,  it  would  follow 
that  the  ratios  of  5.2  to  1  and  7  to  1  were  equally 
favorable  to  economy,  and  that  there  is  a  better  ratio 
still,  between  the  two ;  probably,  about  6  to  1. 


LENGTH  TO  DEPTH  OF  TRUSS.  103 

But  the  conditions  arc  not  the  same  in  the  two  cases, 
aside  from  the  different  values  of  v.  For,  while  with 
v=/i,  the  diagonals  incline  at  45°,  in  the  other  case, 
their  inclination  from  the  vertical  is  considerably  less, 
being  only  about  37°.  This,  we  shall  see  hereafter,  is 
a  less  favorable  inclination  for  diagonals  acting  by  ten 
sion,  than  45°;  and,  since  the  ratio  of  5.2  to  1  shows 
an  equality  as  to  economy,  with  the  ratio  of  7  to  1, 
with  the  more  favorable  conditions  on  the  side  of  the 
latter,  it  would  seem  at  least,  highly  probable  that  the 
ratio  of  5.2  to  1  is  the  more  near  approximation  to  the 
desired  optimum. 

No\v,  after  much  thought  and  investigation,  with 
some  considerable  experience  in  planning  and  con 
structing  truss  bridges,  I  can  give  no  better  pra  ticai 
rule  as  to  the  proper  depth  of  a  truss  of  a  given  length, 
than  to  adopt  that  ratio  between  7  to  1  and  5  to  1, 
which  will  best  accommodate  the  desired  length  of 

O 

panel  (or  value  of  A),  and  afford  the  best,  and  most 
economical  inclination  of  diagonals;  matters  to  which 
attention  will  shortly  be  directed. 

It  is  not  supposed,  however,  that  these  limits  of 
ratio  will  not  frequently  be  exceeded,  particularly  in 
the  adoption  of  a  greater  ratio  than  7  to  1.  In  case 
of  the  very  long  spans  dared  and  achieved  in  this  age 
of  rail  roads  and  locomotion,  engineers  may  recoil  from 
the  towering  altitudes  of  50  or  60  feet  depth  of  truss 
which  some  of  the  long  spans  now  occasionally  con 
structed  would  require,  perhaps  more  in  deference  to" 
European  precedent,  and  from  an  instinct  of  conserva 
tism,  than  from  regard  to  economy,  and  a  true  appre 
ciation  of  the  real  merits  of  the  question.  But  for 
important  bridges  for  heavy  burthens,  a  ratio  greatei 


104        ,  BRIDGE  BUILDING. 

than  8  to  1  can  not  be  regarded  as  commendable,  ex 
cept  in  rare  and  peculiar  circumstances. 

INCLINATION  OF  DIAGONALS. 

LXV.  We  have  seen  the  absolute  importance  of  ob 
lique  members  in  bridge  trusses,  and  we  have  also 
seen  the  excellence,  in  point  of  theoretical  economy, 
of  the  trapezoidal  truss,  with  parallel  chords  con 
nected  by  diagonal  members,  with  or  without  verticals. 
Now,  since  there  is  an  endless  variety  in  the  positions 
which  a  diagonal  member  may  assume,  it  becomes  an 
important  question,  what  degree  of  inclination  these 
members  should  have,  to  give  the  most  economical  and 
satisfactory  results. 

The  inclination  may  be  increased  till  it  reaches  a 
horizontal  position,  or  diminished  till  it  becomes  a  ver 
tical  ;  when,  in  either  case,  the  member  ceases  to  be  a 
diagonal,  and  becomes  incapable  of  performing  the 
office  of  effecting  a  horizontal  transfer  of  vertical  pres 
sure. 

The  greatest  efficiency  of  material  used  in  diagonals, 
is  manifestly,  when  the  weight  sustained  by  a  given 
quantity  of  material,  multiplied  by  the  horizontal 
reach,  gives  the  largest  product ;  and,  wrhen  the  mem 
ber  acts  by  tension,  the  weight  capable  of  being  sus 
tained  by  a  given  amount  of  material,  is  as  the  cross- 
section  directly,  and  as  the  rate  of  strain  inversely. 
But  the  rate  of  strain,  or  stress  produced  by  a  given 
weight,  is  as  the  weight  multiplied  by  the  length  of 
diagonal  (D),  and  divided  by  the  vertical  (y),  or  as  — » 

while   the   cross-section   is   inversely   as   D,   or   as  — 
Hence,  the  weight  is  as   -  -s-  D,  =  V3. 


INCLINATION  OF  DIAGONALS.  105 

Now,  representing  the  horizontal  reach  by  h,  the 
efficiency   of   the    material    must   be    as   -|  equal  to 

~5"X»-     Then,  making  v,  constant,  and  dividing  by  v, 


the  expression  becomes,  -a—~,  still  being  proportional 
to  the  efficiency  of  material.  Consequently,  that  value 
of  h,  which  gives  the  largest  value  to  the  expression 
wiH  indicate  the  inclination  at  which  the  diago 


nal  will  act  with  the  greatest  efficiency. 

This  value  of  A,  is  found  by  differentiating  the  func 
tion  -rrra»  (h  being  the  variable),  and  putting  the  dif 
ferential  equal  to  0  :  by  which  process  we  obtain  : 

<*  (?£*)  =(-^5r^=°'  whenee  ca"celil's  the 

denominator,  v2d'h  +  h2dh  =  2/i2d/>,  and  h2dh  =  v2dh* 
Then,  dividing  by  dA,  and  extracting  the  square  root, 
we  have  h=u  ;  thus  showing  that  an  inclination  of 
45°  is  the  most  advantageous  for  tension  diagonals  as 
far  as  relates  to  those  members  alone. 

THRUST  DIAGONALS. 

LXYI.  The  efficiency  of  material  in  a  thrust  brace, 
is  directly  as  the  useful  effect  produced  by  the  member, 
and  inversely  as  the  amount  of  material  required  in  it. 

Now,  the  useful  effect,  as  in  the  previous  case,  is 
as  the  weight  sustained  and  the  horizontal  reach,  while 
the  amount  of  material,  depends  not  only  upon  the 
stress  and  length,  but  also  upon  the  ratio  of  length  to 
diameter,  which  affects  the  power  of  resistance. 

Theoretically,  the  power  of  resistance  is  as  the  cube 
of  the  diameter  (d),  divided  by  the  square  of  the  length 
(=i;2xA2),  a  rule  which  is  not  sustained  by  experience, 

*  d(Roman),  before  a  variable,  or  the  function  of  a  variable,  denotes 
the  differential  of  such  variable  or  function. 

14 


106  BRIDGE  BUILDING. 

except  in  case  of  long  slim  pieces  which  break  by 
lateral  deflection,  under  a  comparatively  small  com- 
pressive  force.  We  will,  however,  use  the  rule  for  the 
present  occasion. 

The  efficiency  of  the  material  then,  will  be  as  the 
power  of  resistance  and  the  horizontal  reach  directly, 
and  as  the  stress  produced  by  a  given  weight,  in 
versely  ;  which  stress  is  as^li^L.  "Whence  we  have 

V 

_^_^_v/^+P  (       ^    )  proportional  to  the  efficiency 

of  material  in  a  thrust  brace.  Making  6^=1,  the  last  ex 
pression  becomes  A  ,  and  the  value  of  A  which  gives 

the  greatest  value  to  this  function,  will  indicate  the 
inclination  at  which  a  thrust  brace  will  act  with  the 
greatest  efficiency,  as  it  regards  the  brace  alone. 
Differentiating,  and  putting  the  result  equal  to  0,  we 
have  : 

d  (      h     }  =dh  lpa  +  h*]  *-*h  (g'+^  *  X2ftdA_ Q  •  whence 

V+^)r  (tfH-/**)1 

multiplying  by  the  denominator  (i^+A2)8,  we  obtain 
dh  (vz+h2)*  =  §  A  (v2  +  A2)J  X  2MA,  and,  dividing  by 
x/(v2+ A2)dA,  we  have  v2+ h2  =  f  Ax2A  =  3A2  whence,  v2  = 
3A2_/j2  ^  ^h^  and  by  evolution,  v  =  A>/2,  and  h  =-^ 
=  0.7072y. 

If  we  deduce  the  value  of  the  expression  *.  |? 
(which  is  equal  to  the  horizontal  reach  divided  by  the 
cube  of  the  length  of  brace),  putting  h—v  and  A=Jy 
successively,  we  find  the  degree  of  efficiency  less  than 
the  maximum,  as  above  determined,  by  about  9  per 
cent  in  the  former,  and  8  per  cent  in  the  latter  case  ; 
showing  that  considerable  deviations  may  be  made  in 
the  inclinations  of  thrust  braces  without  much  detri 
ment  to  efficiency  of  material  in  braces,  when  required 


INCLINATION  OF  DIAGONALS. 


107 


by  other  considerations ;  which  will  often  be  the  case, 
as  will  be  seen  hereafter. 


EFFECTS  OF  INCLINATION  OF  DIAGONALS  UPON  STRESS  OF 
CHORDS  AND  VERTICALS. 

LXVII.  The  comparative  effects  of  different  posi- 
sitions  of  diagonals  upon  the  chords,  may  be  illustrated 
with  reference  to  Fig.  21.  It  is  manifest  that  a  given 
weight  w  on  the  centre  of  this  truss,  will  produce  a 
vertical  pressure  equal  to  %w  at  each  of  the  points 
a  and  6,  and  that  each  oblique  member  between  a  and  iv, 
will  sustain  a  weight  equal  to  Jw;  and  will  exert  each 
a  horizontal  action  upon  the  upper  and  lower  chords, 
equal  to  JM/.  Hence,  the  stress  of  chords  in  the  centre, 

will  equal  %w  xn,  in  which  n  represents  the  number 
of  oblique   members  between  a  and  w,  or  between 


ac 


a  and  c.     But  n  equals  ^whence  \w  ln  =  ^w- 

a  *  9        z    V 


The  term  h  having  been  eliminated  from  the  last  ex 
pression,  it  shows  that  the  inclination  of  diagonals  has 
no  effect  upon  the  stress  of  chords  in  the  centre,  pro 
duced  by  weight  in  the  centre  of  the  truss ;  and  by 
similar  reasoning  it  is  shown  that  the  same  is  true  in  re 
lation  to  other  parts  of  the  chords,  or  to  weight  at  any 
other  points  in  the  length  of  the  truss ;  the  only  differ 
ence  being  that  the  shorter  the  panels,  or  the  smaller 


108  BRIDGE  BUILDING. 

the  value  of  A,  the  shorter  the  intervals  at  which  the 
increments  in  the  stress  of  chords  are  added,  and  the 
less  the  magnitude  of  such  increments,  in  the  same 
proportion.  Hence,  in  general,  there  is  no  difference 
in  the  stresses  of  chords,  whether  the  diagonals  have 
one  inclination  or  another. 

With  regard  to  the  effect  upon  verticals,  that  part 
of  their  stress  which  they  receive  through  diagonals, 
is' equal  to  the  weight  sustained  by  those  diagonals, 
and  is  the  same  for  a  given  weight,  whatever  be  their 
inclination.  On  the  vertical  we,  the  pressure  is  re 
ceived  directly  from  the  weight.  But  on  the  next  ad 
jacent  vertical,  on  either  side,  one-half  of  the  same 
pressure  is  received  through  to  the  intervening  diago 
nal,  and  transmitted  to  the  next,  and  so  on  to  the  end. 

Consequently  the  aggregate  action  of  verticals,  pro 
duced  by  the  weight  w,  is  equal  to  w  -f  \wn,  taking  n 
for  the  number  of  verticals  receiving  their  stress 
through  the  medium  of  diagonals,  and  which  is  equal 
to  the  whole  number  less  3,  when  the  number  is  odd, 
and  the  verticals  act  by  thrust,  as  assumed  in  the  case 
of  Fig.  21.  If  the  weight  be  applied  at  the  lower 
chord,  the  whole  action  of  verticals  is  communicated 
through  diagonals,  the  latter  acting  by  tension. 

Hence  the  aggregate  action  of  verticals  increases  and 
diminishes  with  their  number,  and  economy  as  regards 
those  members,  would  require  the  diagonals  to  incline 
at  a  greater  angle  with  the  vertical  than  that  which 
is  most  favorable  as  to  the  diagonals  themselves. 

We  have  seen,  however  [LXVI]  that  by  placing  the 
diagonals  at  45°  when  they  act  by  thrust,  we  lose  about 
9  per  cent  in  economy  of  those  members,  and  we  now 
learn  that  such  an  arrangement  increases  the  economy 
in  verticals  to  a  considerable  extent  by  diminishing 


WIDTH  OF  PANEL.  109 

their  number ;  the  actual  amount  depending  somewhat 
upon  the  number,  and  not  deducible  by  a  general  rule. 

We  shall  not,  however,  err  greatly  in  assuming,  that 
with  an  inclination  of  45°,  for  thrust  diagonals  in  con 
junction  with  tension  verticals,  the  loss  upon  the 
former  is  quite  made  up  by  saving  in  the  latter,  and 
that  a  less  inclination  in  this  case,  should  be  regarded 
as  very  questionable  practice. 

In  case  of  tension  diagonals  and  vertical  struts,  a 
saving  in  material  may  undoubtedly  be  made  by  mak 
ing  the  horizontal  greater  than  the  vertical  reach  of 
the  diagonal,  whenever  such  a  course  is  found  consist 
ent  with  a  proper  regard  to  just  proportions  of  the 
truss  in  other  respects ;  such  as  width  of  panel,  depth 
of  truss,  etc. 

THE  WIDTH  OP  PANEL. 

LXVIII.  Which  we  have  represented  in  our  formu 
lae  by  A,  has  only  been  hitherto  considered  as  to  its 
relations  to  v,  representing  the  depth  of  truss. 

With  regard  to  the  best  absolute  value  of  A,  .the  ques 
tion  is  affected  by  the  relative  expense  of  floor  joists, 
and  the  extra  amount  of  material  and  labor  in  forming 
connections  at  the  nodes  of  the  chords ;  as  well  as,  in 
some  cases,  the  lengths  of  sections  in  the  upper  chord. 
The  latter  requires  support  laterally  and  vertically  at 
intervals  of  moderate  length,  depending  upon  the  ab 
solute  stress,  which,  other  things  the  same,  governs  the 
cross-section. 

The  upper  chord  usually,  of  whatever  material,  has 
a  cross-section  so  large  as  to  exclude  all  danger  of 
breaking  by  lateral  deflection,  in  sections  of  10  to  14 
feet ;  and,  as  there  will  seldom  be  occasion  for  exceed 
ing  these  lengths  in  cancelated  trusses,  the  increased 


110  BRIDGE  BUILDING. 

expense  of  joists  for  wide  panels,  and  the  expense  of 
extra  connections  in  narrow  ones,  are  the  principal 
considerations  affecting  the  absolute  value  of  A,  as  an 
element  of  economy. 

The  transverse  beams,  supposed  to  be  located  at  the 
nodes  between  adjacent  panels,  may,  of  course,  be  pro 
portioned  to  the  width  of  panel,  so  as  to  require  essen 
tially  the  same  material  in  all  cases.  But  the  joists,  or 
track  stringers  of  rail  road  bridges,  the  depth  being 
proportional  to  the  length  between  supports,  have  a 
supporting  power  as  their  cross  sections;  and  since  the 
load,  at  a  given  weight  to  the  lineal  foot,  is  directly  as 
the  length,  it  follows,  that  to  support  the  same  load  per 
foot,  as  bridge  joists  are  required  to  do,  the  cross-sec 
tion  should  b£  as  the  length.  The  expense  of  joists 
and  stringers,  therefore,  is  directly  as  the  width  of 
panel.* 

On  the  contrary,  the  expense  of  connections 
will  be  as  the  number  of  panels,  nearly,  and  conse 
quently,  inversely  as  their  width,  or  inversely  as  the 

*The  thickness  of  joist  most  economical  for  a  short  reach  would  be 
liable  to  buckle  with  greater  length  and  depth.  Hence  joists  require 
increase  of  thickness  with  increase  of  length  and  depth.  The  thick 
ness  should  be  as  the  depth,  and  the  cross-section,  as  the  square  of  the 
depth  (d). 

Upon  this  basis,  the  required  material  for  joists,  increases  at  a  greater 
ratio  than  the  increase  in  width  of  panels.  The  supporting  power  of  a 
joist  or  beam  of  a  given  form  of  section,  or  a  given  ratio  of  depth  to 
thickness,  is  as  the  cube  of  the  depth  directly,  and  the  length  (I)  in 
versely  ;  or,  as  -y.  If  there  be  two  joists  of  depths  respectively  as  d  and  x, 
and  lengths  as  I  and  nl,  their  supporting  powers  P,  P7,  for  load  simi 
larly  applied,  will  be  as-j-  to  ~.  But  the  power  should  be  as  the  load  ; 
in  other  words,  as  the  length  of  joists.  Hence  we  have  the  proportion, 
-.-  :  —.  : :  I :  nl,  whence,  nd*  ——  and  x  =»  dn$ .  Now  n  is  as  the  length 

of  joists,  and  the  depth,  therefore,  is  as  the  f  power  of  the  length,  and 
the  cross-section,  and  consequently  the  required  material,  .as  the  ^ 
power  of  the  length.  Hence,  if  m  represent  the  material  for  joists 
with  panels  of  a  given  width,  the  material  for  panels  twice  as  wide, 
will  be  represented  by  m  X  xj/2*=m^r  16  =  m2.52.  But  this  is  rather 
anticipating  the  subject  of  lateral,  or  transverse  strength  of  beams. 


WIDTH  OF  PANEL.  Ill 

length  of  joists.  Hence,  if  we  could  find  the  point 
where  the  cost  of  connections  (consisting  of  extra 
material  in  the  lappings  of  parts,  connecting  pins, 
screws  and  nuts,  and  enlarged  sections  at  the  ends  of 
members,  together  with  the  extra  labor  in  forming  the 
connections),  becomes  equal  to  the  whole  cost  of  ma 
terial  in  joists  or  stringers  ;  that  would  seem  to  indi 
cate  the  proper  width  of  panel,  or  value  of  A,  as  far  as 
depends  upon  these  elements. 

But  aside  from  the  fact  that  our  data  upon  this 
question  are  so  few  and  so  imperfect,  that  it  would  be 
mere  charlatanism  to  attempt  to  reduce  the  matter  to 
a  mathematical  formula,  the  occasions  would  be  so 
rare  which  would  admit  of  the  application  of  such 
formula,  without  incurring  disadvantages  in  other  re 
spects,  such  as  improper  inclination  of  diagonals,  un 
suitable  ratio  of  length  to  depth  of  truss,  &c.,  that  no 
attempt  will  be  here  made  to  give  any  thing  more 
definite  upon  thfl  point,  than  to  refer  to  the  best  pre 
cedents  and  practice  of  the  times;  which  seem  to  con 
fine  the  range  of  width  of  panel  mostly  within  the 
limits  of  8  and  15  feet. 

Within  these  limits,  and  seldom  reaching  either  ex 
treme,  plans  may  be  adapted  to  any  of  the  ordinary 
lengths  of  span,  by  adopting  the  single  or  double  can- 
celated  trusses,  Figs.  12  and  13,  or  18  and  19,  or  the 
arch  truss  Fig.  11,  (which  unquestionably  contain  the 
essential  principles  and  combinations  of  the  best  trusses 
in  use),  according  to  length  of  span,  the  purposes  of 
the  bridges  respectively,  or  the  taste  and  judgment  of 
engineers  and  builders. 


112  BRIDGE  BUILDING. 


ARCH  BRIDGES. 

LXIX.  An  arch  bridge  may  be  distinguished  from 
an  Arch  Truss  Bridge,  by  the  fact  that  in  the  former,  the 
bridge  and  its  load  are  sustained  by  one  or  more  arches 
without  chords  ;  and,  consequently,  requiring  external 
means  to  withstand  the  horizontal  thrust  or  action  of 
the  arches  at  either  end  ;  which  means  are  afforded  by 
heavy  abutments  and  piers,  in  case  of  erect  arches,  and 
by  towers  and  anchorage  in  the  earth,  in  case  of  in 
verted,  or  suspension  arches. 

It  is  not  the  purpose  of  this  work  to  treat  elaborately 
of  either  of  these  forms  of  bridging,  as  the  author's 
experience  and  investigations  have  been  mostly  con 
fined  to  truss  bridge  construction.  But  as  some  of  the 
largest  bridge  enterprises  and  achievements  of  the  age 
are  designed  upon  the  principles  hiMje  referred  to,  a 
brief  notice  of  the  subject,  and  some  of  the  conditions 
affecting  the  use  of  these  classes  of  bridges,  may  be 
regarded  as  desirable  in  a  work  of  this  kind. 

Suspension,  or  inverted  arch  bridges  of  very  great 
spans,  have  long  been  in  use,  both  in  this  and  foreign 
countries ;  and  the  capabilities  of  that  system  have  been 
pretty  thoroughly  tested  experimentally  and  practically. 

But  bridges  supported  by  erect  metallic  arches,  have 
hitherto  been  confined  to  structures  of  moderate  span. 
Within  a  few  years,  however,  the  magnificent  enter 
prise  of  spanning  the  Mississippi  at  St.  Louis  by  three 
noble  stretches  of  about  500  feet  each,  supported  each 
by  four  arched  ribs  of  cast  steel,  has  been  undertaken 
and  is  understood  to  be  in  rapid  process  of  execution. 
The  interest  naturally  felt  in  the  progress  and  final 
result  of  this  grand  enterprise,  by  students  and  practi- 


ARCH  BRIDGES. 


113 


tioners  in  the  engineering  profession,  will  perhaps  aid 
in  rendering  the  following  brief,  and  somewhat  super 
ficial  discussion  acceptable. 

LXX.  An  erect  arch  subjected  to  the  action  of 
weight,  or  vertical  pressure,  is  in  a  condition  of  unsta 
ble  equilibrium ;  and  can  only  stand  while  the  weight 
is  so  distributed  that  all  the  forces  acting  at  each  point 
of  its  length,  are  in  equilibrio.  To  illustrate  this,  we 
may  assume  the  arch  to  be  composed  of  short  straight 
segments  meeting  and  forming  certain  angles  with 
one  another,  and  the  weights  applied  at  the  angular 
points. 

A  weight  at  <?,  Fig.  22,  for  instance,  acts  vertically, 
and,  if  dc  be  produced  till  it  meet  the  vertical  drawn 

FIG.  22. 


L 


through  b  in  w,  then  the  triangle  bcm  has  its  sides 
respectively  parallel  with  the  directions  of  three  forces 
acting  at  the  point  <?;  namely,  the  weight  at  the  point 
c,  the  thrust  of  the  segment  6c,  and  that  of  dc.  Hence, 
if  these  three  forces  be  to  one  another  as  the  sides  of 
said  triangle, — that  is,  if  the  weight  (w) :  thrust  of  be  : 
thrust  of  dc :  :  bm :  be :  cm,  then  they  are  in  equilibrio. 
If  w  be  greater  than  is  indicated  by  this  proportion, 
the  point  c  will  be  depressed,  bed  approaching  nearer 
and  nearer  to  a  straight  line,  and  becoming  less  and 
15 


114  BRIDGE  BUILDING. 

less  able  to  support  the  weight,  and  a  collapse  must 
result. 

If  w  be  less  than  the  above  proportion  indicates,  it 
will  be  unable  to  withstand  the  upward  tendency  of 
the  point  c,  due  to  the  thrust  of  be  and  dc  (or,  to  the 
preponderance  of  the  vertical  thrust  of  6c,  over  that  of 
dc),  the  point  c  will  rise,  the  upward  tendency  becom 
ing  greater  and  greater,  and  the  result  will  be  a  col 
lapse,  as  before.  The  same  reasoning,  and  the  same 
inference,  apply  to  any  other  angular  point,  as  at  c. 
It  is,  therefore,  only  in  theory  that  such  a  thing  as  an 
equilibrated  erect  arch,  can  exist.  The  arch  is  here 
considered  as  a  geometrical  line  without  breadth  or 
thickness. 

It  is  this  property  of  instability,  in  the  Erect  Arch, 
that  the  diagonals  in  the  Arch  Truss,  [Figs.  5  and  11] 
are  designed  to  obviate,  and  to  enable  the  arch  to  re 
tain  its  form  and  stability  under  a  variable  load. 

LXXI.  Still,  in  theory,  an  arch  maybe  in  equilibrio 
with  any  given  distribution  of  load,  whenever  the  points 
a,  6,  c,  etc.,  are  so  situated  that  the  sides  of  the  trian 
gle  bcm,  for  instance,  formed  by  a  vertical  with  lines 
respectively  coinciding  or  parallel  with  the  two  seg 
ments  meeting  at  c,  are  proportional  to  the  3  forces 
acting  at  c,  as  above  stated,  and  so  at  the  other  angu 
lar  points  of  the  figure. 

To  construct  an  equilibrated  arch  adapted  to  a  given 
distribution  of  load,  consisting  of  determinate  weights 
at  given  horizontal  intervals  between  the  extremities 
of  the  arch,  we  may  proceed  as  follows  : 

Draw  a  horizontal  line  representing  the  chord  ak, 

and  upon  the  vertical  Cft,  erected  from  its  centre,  take 

.  Cf  equal  to  the  required  versed  sine,  or  depth  of  the 


I 

ARCH  BRIDGES.  115 

arch  at  the  centre.  Also,  take//=Qr,  and  erect  verti 
cals  upon  the  chord,  at  all  the  points  at  which  the  load 
is  applied,  and  join  a  and  t. 

Then,  if  the  load  be  uniformly  distributed  (horizon 
tally)  upon  the  arch,  we  have  seen,  [LII],  the  arch 
should  be  a  parabola,  to  which  of  course,  at  is  tangent 
at  the  extremity,  a.  But,  regarding  ab  as  tangent  to 
the  curve  at  r,  half  way  between  a  and  b  (horizontally), 
we  seek  the  abscissa  /$,  which  is  to  Cf: :  rs2 :  aC2. 
Then,  taking  the  distance  of/w=/s,  au  is  tangent  to  the 
curve  at  r,  and  coincides  with  the  first  segment  (ab)  of 
the  arch.  (These  segments  are  supposed  to  be  so 
short,  that  the  tangent  and  curve  may  be  regarded  as 
essentially  coinciding,  for  the  length  of  a  single  segment) . 

Now,  the  thrust  of  ab,  is  to  the  whole  weight  bear 
ing  at  a,  as  ru  to  us  ;  and,  erecting  the  vertical  al,  such 
that  al :  ab:  :  weight  at  b  :  thrust  of  a£,  and  drawing 
the  straight  line  Ibc,  cutting  the  second  vertical  in  c,  we 
have  be  for  the  second  segment  of  the  arch,  being  in 
the  line  of  £6,  which  represents  the  resultant  of  the  two 
forces  acting  at  b ;  namely  the  weight  at  b,  and  the 
thrust  of  ab. 

In  like  manner,  take  6m,  representing  the  weight  at 
c,  and  the  straight  line  mcd,  meeting  the  third  vertical 
in  dj  gives  cd  as  the  third  segment  of  the  arch. 

Kepeat  the  same  operation  for  each  of  the  succeed 
ing  segments  de,  ef,  &c.,  till  the  arch  is  completed,  and 
it  is  obvious  that  the  forces  acting  at  each  of  the  several 
angular  points  6,  c,  d,  &c.,  are  in  equilibrio ;  and  that 
the  arch  throughout  is,  theoretically,  in  a  state  of 
equilibrium. 

We  may  vary  this  process  so  as  to  secure  greater 
accuracy  of  construction,  in  the  following  manner  : 


116  BRIDGE  BUILDING. 

Producing  Ibc  till  it  meets  Ct  in  y,  we  see  that  abl  and 
ubv  are  similar  triangles,  and  al :  uv  : :  horizontal  dis 
tance  of  I :  horizontal  distance  of  v,  from  the  point 
b.  Hence,  we  may  take  the  point  v  instead  of  the  point 
I,  by  which  to  establish  the  position  of  the  line  be,  and 
thereby  secure  greater  relative  accuracy  of  measure 
ment. 

So  may  we  also  take  m',  or  IV  instead  of  bm,  to  de 
termine  the  line  cd.  By  this  means  we  multiply  the 
small  spaces  al,  bm,  &c.,  and  diminish  the  amount  of 
error  in  measurement,  and  if  the  angular  points,  or 
nodes  be  at  uniform  horizontal  distances,  the  process  is 
very  simple. 

LXXII.  We  have  assumed,  in  describing  the  arch 
a,  6,  c,  <Y,  &c.,  a  uniform  distribution  of  load,  horizon 
tally.  But  the  general  process  is  obviously  the  same 
for  an  unequal  distribution,  after  locating  the  first  seg 
ment  ob ;  which  we  may  do  by  first  ascertaining  the 
amount  of  bearing  at  <2,  due  to  the  load  of  the  arch. 
This  will  be  to  the  whole  load,  as  the  distance  of  the 
centre  of  gravity  of  load  from  &,  horizontally,  to  the 
whole  chord  ak.  For  instance,  if  the  centre  of  gravity 
be  halfway  between  C  and  A',  one  quarter  of  the  load 
bears  at  a.  The  weight  bearing  at  #,  whatever  it  be, 
may  be  represented  by  A;  and  supposing  it  to  exert 
the  same  horizontal  thrust  at  a  as  half  the  load  (W), 
would  do  when  uniformly  distributed,  we  take  u'  in 
ft,  so  that  J  W  :  A  : :  uC:  u'C*  Then  auf  gives  the 
direction  of  «&',  and  we  proceed  in  the  same  manner 

*  We  may  assume  any  amount  of  horizontal  thrust,  and  the  greater 
the  assumed  thrust,  with  a  given  load,  the  less  will  be  the  depth  of 
the  arch,  and  vice  versa.  It  is  proposed  here  to  construct  an  equili 
brated  arch  a',  b,'c',  dj&c,,  of  about  the  same  rise  at  the  crown,  as  the 
jiormal  curve,  a,  b  c,  d,  &c.,  has. 


ARCH  BRIDGES.  117 

as  before  using  the  weights  given  for  the  several  nodes 
of  the  arch,  to  determine  the  points  c',  df,  &c.  These 
being  connected  by  straight  lines,  we  have  an  equili 
brated  arch  adapted  to  the  given  distribution  of  load. 

LXXIII.  But  of  course,  this  arch  will  not  stand 
under  any  other  disposition  of  the  load.  To  obviate 
this  difficulty,  and  to  construct  an  arch  which  will 
stand  under  a  variable  load,  without  the  chord  am? 
counter-bracing  of  the  arch  truss,  the  device  has  been 
adopted,  of  constructing  the  arch  of  such  vertical  width 
that  all  the  equilibrated  arches  or  curves,  required  by 
all  possible  distributions  of  load;  may  be  embraced 
within  the  width  of  the  arched  rib.  Then,  if  there  be 
sufficient  material  to  oppose  and  withstand  tjie  forces 
liable  to  act  in  the  lines  of  said  several  equilibrated 
curves,  complete  vertical  stability  must  result. 

The  proper  width,  or  depth  of  the  arched  rib,  will 
depend  upon  the  length  and  versed  sine  of  the  arch, 
as  well  as  the  amount  and  distribution  of  load ;  and 
the  material  will  act  most  efficiently,  when  mostly  dis 
posed  in  the  outer  and  inner  edges,  or  members  of  the 
rib,  and  connected,  either  by  a  full,  or  an  open  web,  to 
distribute  the  action  between  the  outer  and  inner  mem 
bers,  according  as  the  resultant  line  of  action  approaches 
the  one  or  the  other  of  those  members. 

The  normal  form  of"  the  arch  should  be  such  as  to 
be  in  equilibrio  under  a  uniform  load,*  and  hence  it 
will  be  parabolic,  as  to  the  movable  load,  and  the 
weight  of  road-way,  and  catenarian,  as  to  the  weight 

*  The  method  above  explained,  for  describing  an  equilibrated  arch, 
is  applicable  to  all  cases  where  the  load,  both  constant  and  variable 
acting  on  the  several  parts  of  the  arch,  is  known,  whether  it  be  the 
normal  curve,  adapted  to  a  full  load,  or  a  distorted  curve,  suited  to  an 
irregular  distribution  of  load. 


118  BRIDGE  BUILDING. 

of  arches  (as  far  as  they  are  uniform  in  section),  and 
should  approach  the  one  or  the  other  form,  according 
to  the  weight  of  arches,  as  compared  with  the  other 
weight  to  be  supported  thereby. 

The  distance  between  outer  and  inner  members,  or 
the  width  of  web,  reckoned  from  centre  to  centre  of 
those  members,  should  be  such  that  no  condition  of 
unequal  and  partial  load,  could  throw  greater  action 
at  any  point  of  either  member,  than  the  extreme  uni 
form  load  would  throw  upon  both. 

Let  us  suppose  that  the  curve  a,  5,  <?,  d,  etc.,  be  cen 
trally  between  the  two  members  and  that  ddf,  and  hhf 
be  the  greatest  vertical  departures,  in  ward  and  outward, 
of  any  equilibrated  curve,  from  the  normal  curve  a,  6, 
c,  etc. 

Let  us  further  suppose  that  the  thrust  of  the  arch 
at  the  points  d  and  A,  be  }  as  great  under  the  load  act 
ing  in  the  curve  of  greatest  departure  from  the  normal 
as  the  extreme  uniform  load  produces  at  those  points. 
Then,  if  the  outer  and  inner  members  of  the  rib,  be 
placed  at  a  distance  of  six  times  the  greatest  departure 
of  the  distorted  from  the  primary,  or  central  curve, 
one  member  will  be  twice  as  far  from  the  line  of  action 
(at  the  point  of  greatest  departure),  as  the  other,  and 
the  latter  will  sustain  two-thirds  of  the  action,  equal 
to  one-half  the  action  of  the  full  load,  and  the  same  aa 
in  the  latter  case. 

If  the  width  of  web  be  less  than  six  times  the  great 
est  aberration  of  the  distorted  curve,  the  action,  under 
the  suppositions  above,  will  be  greater  upon  one  mem 
ber  than  that  due  to  a  full  uniform  load  ;  a  condition 
altogether  to  be  avoided. 

A  few  trials  at  constructing  curves  adapted  to  as 
sumed  possible  distributions  of  load,  may  determine 


ARCH  BRIDGES.  119 

satisfactorily  what  condition  gives  the  curve  of  great 
est  distortion  and  the  greatest  departure  from  the  nor 
mal  ;  and  the  amount  of  action  under  that  condition, 
can  be  readily  calculated  with  sufficient  nearness, 
whence  the  proper  width  of  web  may  be  deduced. 

LXXIV.  The  points  of  the  equilibrated  curve  may 
be  located  by  calculation,  and  perhaps  with  as  much 
ease,  and  greater  accuracy  than  by  construction. 

Suppose  Fig.  22  to  have  a  vertical  depth,  Cf,  equal 
to  one  of  ten  equal  sections  of  the  chord  ak.  Having 
found  the  length  of/tf,  in  the  manner  already  explained 
[LXXI],  it  is  known  that  for  a  uniform  loud  at  each 
angle,  the  vertical  reaches  of  the  several  segments, 
begining  at  the  centre,  are  as  the  odd  numbers,  1,  3,  5, 
7  and  9 ;  and,  if  we  conceive  Cf  to  be  divided  into  25 
equal  parts  (25  being*  the  sum  of  these  numbers),  each 
of  these  parts  will  be  equal  to  0.04G/,  or  .04^;  and  this 
factor,  multiplied  by  the  numbers  1,  3,  5,  &c.,  give  the 
vertical  reaches  of  the  respective  straight  segments, 
which  vertical  reaches  being  substracted  successively 
from  v,  and  successive  remainders,  show  the  several 
verticals  to  be  as  follows:  At  the  centre,/,  vertical  = 
Cf=v.  At  e,  vertical  —v  —  .04y  =  .96y.  At  d,  verti 
cal  =  (.96— .12)i?  =  .84y;  at  c,  vertical  =  (.84— .2)y  = 
.64*?,  and  at  6,  vertical  =  (.64— .28)u,  =  .36v.  This  es 
tablishes  the  normal  curve  for  uniform  load. 

Now,  supposing  the  weight  of  structure  to  be  equal 
to  Iw  at  each  of  the  angles  of  the  arch,  and  also,  that 
a  movable  load  of  a  like  weight,  w,  be  acting  at  each 
of  the  five  points/,  g,  h,  i,j  ;  the  permanent  weight  of 
structure  gives  a  bearing  of  4.5w;  at  a,  and  the  movable 
weights  at  /,  #,  A,  &c.,  give  respectively  .5w,  Aw,  .3w, 


120  BRIDGE  BUILDING. 

.2i#,  and  ,1?0,  together,  equal  to  1.5w  ;  making  the 
whole  bearing  at  «,  equal  to  6w;,  which  is  £th  less  than 
if  the  same  weight  were  distributed  uniformly. 

Then  taking  Cuf  —  f  Cu,  and  drawing  the  line  aur, 
(not  shown  in  the  diagram),  we  have  the  inclination  of 
abf,  the  first  segment  of  the  required  curve,  which  gives 
the  same  horizontal  thrust  at  <z,  as  the  normal  curve 
would  exert  under  the  same  load  uniformly  distributed. 
We  find/^  (=/s),  by  the  proportion. 

Cfifs::  6V  (=  6?) :  sr2  (=  4^?~ :  :  25*;2 :  20.25-i;2 :  :  v 
:  .81v;  and,  reducing  I.Slv  (=Cu),  by  one-seventh,  we 
obtain  GV  =  1.5514v.  This  length  is  to  aC  : :  A  (=610), 
:  horizontal  thrust  of  ab' ;  that  is  (making  ^=1),  1.5514 

:  5  :  :  Gw  :   ,8?!° ,  =  19.33i0,  =  horizontal  thrust  ab. 

I.ool4 

K'ow,  if  this  thrust  be  represented  by  J-a(7,  =  r=l, 
then  w  will  be  represented  by  a  space  equal  to  Trqo>  = 

.05173,  which  is  equal  to  the  vertical  departure  (D),  of 
b'c'  from  ab'uf.  Knowing  the  value  of  this  departure 
which,  of  course,  is  directly  as  v,  and  inversely  as  a  (7), 
we  can  locate  the  points  e',  d! ,  ef  and/7,  by  their  verti 
cal  distances  from  au',  as  follows  :  The  vertical  at  6',  is 
evidently  equal  to  Jxl.5514,  =  .31026;  consequently, 
the  vertical  ate'  =  2x. 31026  — .05173  =  .56879.  Ver 
tical  at  d'  =  3x. 31026— 3X.05173  =  .77559.  Vertical 
e'  =  4x. 31026— 6X.05173  =  .93068,  and  the  vertical  at 
/*,  equals  5X.31026— 10x.05173  =  1.034,  showing  that 
the  new  curve  crosses  the  normal,  between  e  and/,  and 
/'  is  above/,  but  not  shown. 

Then,  if  each  of  the  segments  6V,  cfdf,  &c.,  be  pro 
duced  to  meet  the  indefinite  vertical  drawn  through  a, 
they  will  evidently  cut  that  line  at  intervals  of  D,  2D, 
3D  and  4D  together,  equal  to  10  D,  =  .5173.  Then, 


ARCH  BRIDGES.  121 

the  weight  at/ being1  equal  to  2i0,  it  follows  that  f'gf 
makes  twice  the  deflection  from  e'f  that  the  latter 
makes  from  d'e\  that  is,  equal  to  2D  in  the  horizontal 
distance  of  It1,  or  1,  or  10D  (==  .5173),  in  the  distance 
a (7,  or  5.  Hence,  fg'  produced,  cuts  the  vertical  at  «, 
twice  as  high  as  e'f  cuts  it,  or,  at  a  point  1.0346  above 
a;  being  just  as  high  as  the  point/';  except  a  small 
difference  resulting  probably  from  omitted  fractions. 
This  shows  that  f'g1  is  horizontal,  and  tangent  to  the 
curve  at  its  vertex. 

It  follows  that  all  the  weight  at/,  and  at  the  left  of 
that  point,  is  brought  to  bear  at  «,  and  all  that  at  y' ', 
and  on  the  ri^ht  thereof,  bears  at  k.  This  affords  a 

O  * 

check  upon  our  work  thus  far,  as  we  already  knew 
that  the  bearing  at  a  was  equal  to  Qw,  and  we  now  see 
that  this  is  made  up  of  ~Lw  at  each  of  the  four  points 
£/,  c',  d' ,  e',  and  2w  at  /'.  If/'^'  were  not  horizontal 
the  arch  could  not  be  in  equilibrio  under  the  assumed 
condition  of  load. 

Now,  as  we  manifestly  have  for  the  4  remaining 
segments,  a  vertical  reach  for  each,  as  the  weights 
they  respectively  sustain;  i.  e.,  equal  respectively  to 
2D,4D,6D,and8D;  making  20D  (=00;  altogether,  we 
have  only  to  subtract  these  quantities  successively  from 
Cf  (=1.0346),  to  obtain  the  lengths  of  verticals  at  /*', 
iy,  /' ;  as  follows  : 

1.0346  —  2  x  .05173  =  .93114  =  vert,  at  li' 
.93114^-4  x. 05173  =  .72422=  "  "  if 
.72422  — 6  x. 05173  =  .41384=  "  "/ 
.41384  — 8  X '.05173  =  0  "  "  k 

The  differences  between  these  lengths  of  verticals, 
and  those  of  the  normal  curve  at  the  same  points,  show 

16 


122  BRIDGE  BUILDING. 

the  aberrations  vertically,  of  the  distorted,  from  the  nor 
mal  curve,  as  below. 

Nor.          Dist.  Below.          Above. 

&6'-.86— .81026—.04974  " 

CC'  =.64— .56879=.07121  " 

cM'=.84— .77559=.  06441  « 

eef  =  .96— .93068=.02952  " 

Dist.  Nor. 

ff  =1.034  —1.00=  .034 

#/'=1.034  —  .96=  .07446 

hh'=  .93114-.84=  .09114 

«'  =  ,72422— .64=  .08422 

j/'  =   .41384— .36=  .05384 

LXXV.  From  this  exhibit,  we  perceive  that  the  great 
est  vertical  aberration  externally  for  the  condition  of  load 
here  assumed,  is  at  M',  and  equals  .091?;,  and  the  great 
est  internally,  at  cc'  (or  a  little  to  the  right  of  these 
points  in  both  cases),  equal  to  .071v,  traversing  a  zone 
equal  in  width  to  .162y.  nearly  J  of  the  versed  sine  of 
the  normal  curve. 

Now,  we  have  seen  that  the  horizontal  thrust  of  the 
arch  for  a  gross  load  of  14w,  equals  19.23w,  with  the 
assumed  proportion  of  versed  sine  to  span,  as  1  to  10, 
.  whether  upon  the  normal  or  the  distorted  curve  ;  and, 
the  thrust  being  evidently  as  the  gross  load,  other 
things  the  same,  it  follows  that,  with  the  full  gross 
load  of  18w,  or  2w  at  each  angle,  the  thrust  would  be 
to  19.33w?  as  9  to  7.  Hence  the  load,  as  above  assumed, 
produces  J,  or  77^  per  cent  of  the  maximum  thrust 
under  the  full  uniform  load. 

The  uniform  load  being  supposed  to  act  equally  upon 
the  outer  and  inner  members  of  the  rib,  the  action  of 
50  per  cent  is  due  to  each;  and,  in  order  that  neither 


ARCH  BRIDGES.  123 

member,  at  tbe  nearest  approach  to  the  equilibrated 
curve,  may  be  subjected  to  greater  stress  than  under 
the  greatest  uniform  load,  the  web.  should  be  so  wide 
that  (assuming  the  outward  and  inward  aberrations  to 
be  each  equal  to  the  mean  of  .081v,  and  putting  x  = 
•width  of  web),  x:  Jo:+.081v  :  :  77.7  :  50.  Whence  50z 
=38.88z+77.7x.081w;  and  z=.557tf. 
'  But  this  value  of  a:  being  equal  to  the  distance  verti 
cally  across  the  web  between  c  and  d,  or  between  h  and 
f,  is  greater  than  the  distance  square  across,  about  in  the 
ratio  of  distance  from  a  to/,  to  the  line  aG,  in  this  case 
as-v/26  :  5.  The  actual  width  of  web,  therefore,  is  only 
.545^,  still  considerably  more  than  half  the  versed  sine 
Of. 

The  condition  of  load  here  supposed,  may  or  may 
not  be  the  one  requiring  the  greatest  distortion  of  the 
equilibrated  curve.  The  case  has  been  assumed  to 
illustrate  this  discussion,  as  it  seemed  likely  to  be  near 
the  condition  requiring  the  greatest  width  of  web ; 
and  I  leave  this  part  of  the  subject,  without  attempt 
ing  a  more  general  and  determinate  solution  of  the 
question. 

LXXVI.  The  movable  load  has  been  taken  as  only 
equal  to  the  weight  of  superstructure,  upon  the  suppo 
sition  that  this  style  of  bridging  would  seldom  be 
adopted,  except  for  very  considerable  lengths  of  span, 
where  the  weight  of  superstructure  is  relatively  greater 
than  in  case  of  short  spans. 

This  double  arch,  as  here  under  consideration,  con 
sisting  of  an  outer  and  an  inner  curved  member,  con 
nected  by  a  web,  in  order  to  act  most  efficiently  should 
be  so  adjusted  that  the  outer  and  inner  members  may 
be  subjected  to  equal  action  under  a  full  maximum, 


124  BRIDGE  BUILDING. 

uniform  load.  Hence,  the  normal  and  equilibrated 
curves,  representing  the  line  of  the  resultant  of  forecs 
acting  upon  the  arch,  have  been  assumed  as  terminat 
ing  at  each  end,  at  points  centrally  between  the  ex 
tremities  of  the  outer  and  inner  curved  members. 

It  might  seem  possible  that  the  distorted  curve 
adapted  to  the  above  assumed  condition  of  load,  might 
so  fall  as  to  recross  the  normal  between  the  points  tff 
greatest  departure  and  the  ends,  and  thus  diminish  the 
extent  of  aberration,  and  the  necessary  width  of  web. 
If  the  curve  a,  6',  <?',  etc.,  be  turned  upon  its  centre,  by 
raising  the  end  at  a,  by  f  rc/s  of  the  greatest  departure, 
that  is,  by  -f  x.081v,=.054?;,  the  aberration  half  way 
between  a  and/,  where  it  is  at  or  near  its  maximum 
point,  would  be  reduced  by  .027?;,  and  become  .054y 
just  the  same  as  at  the  end.  The  other  end  would  drop 
to  the  same  extent,  and  would  reduce  the  outward 
aberration  in  the  same  degree.  This,  of  course,  would 
be  the  least  possible  extent  of  aberration ;  and  if  we 
could  rely  upon  the  resultant  stress  following  this  curve 
in  such  a  position,  it  would  enable  us  to  diminish  the 
width  of  web  to  .364y. 

But  there  seems  to  be  no  obvious  reason  why  we 
should  assume  the  equilibrated  curve  to  take  the  posi 
tion  just  described,  rather  than  one  with  the  left  end 
below  a,  and  the  other  above  &,  thus  increasing  instead 
of  diminishing  the  aberration.  Hence,  in  the  case  of 
an  arch  ribbed  bridge,  liable  to  a  movable  load  equal  to 
the  weight  of  structure,  foot  for  foot,  upon  the  whole  or 
any  part  of  its  length,  if  the  web  of  the  ribs  be  less 
than  36-100th,  of  the  versed  sine  (Cf  Fig  22),  certainly, 
and  if  less  than  54-100ths  probably,  the  material  in  the 
principal  members  is  liable  to  greater  strain  in  some 
parts,  under  a  partial,  than  under  the  extreme  load  ; 


ARCH  BRIDGES.  125 

which  would  be  decidedly  an  unfavorable  condition, 
with  regard  to  economy. 

LXXVII.  The  operation  of  the  web  in  distributing 
the  action  upon  the  outer  and  inner  curved  members 
of  the  rib,  and  transferring  it  from  one  to  the  other, 
may  be  understood  by  the  diagram  Fig.  23,  exhibiting 
said  curved  members,  connected  by  a  web  consisting 
of  a  simple  system  of  diagonals,  capable  of  acting  by 
thrust  or  tension  as  may  be  required. 

The  normal  curve  is  represented  parallel  with,  and 
midway  between  the  curved  members  ;  and  the  equili- 

FIG.  23 


brated  curve  is  represented  as  crossing  the  normal 
near/,  meeting  it  again  at  a  and  A:,  at  the  ends;  and 
having  its  greatest  aberrations  at  c  and  A.  It  is  mani 
fest  that  the  action  of  the  outer  member  at  ?,  is  to  that 
of  the  inner  one  atj,  asJA  to  ih  (inversely  as  their  dis 
tances  from  the  distorted  curve),  and  that  the  action 
upon  the  outer  diminishes,  while  that  of  the  inner  one 
increases  each  way  from  i  andj,  until  the  action  upon 
the  two  becomes  equal  at  the  meeting  of  the  curves  at 
k,  and  at  the  crossing  point  near/.  Hence  the  dia 
gonals  leaning  toward  the  point  i  must  act  by  thrust, 
while  those  leaning  fromj,  act  by  tension.  On  the 
contrary  at  d,  where  the  greatest  compression  is  upon 
the  inner  member,  and  diminishes  each  way,  the  dia 
gonals  leaning  from  c,  act  by  thrust,  while  those  lean- 


126  BRIDGE  BUILDING. 

ing  toward  c,  act  by  tension.  The  tension  diagonals 
are  represented  by  single,  and  the  thrust  diagonals,  by 
double  lines. 

But  the  action  changes  more  or  less  with  every 
change  in  the  position  of  the  load,  and  if  the  load  were 
reversed  upon  the  two  halves  of  the  arch,  each  dia 
gonal  here  represented  as  acting  by  thrust,  would  then 
act  by  tension,  and  vice  versa. 

Now,  assuming  that  dc  =  Jce,  and  that  the  action 
upon  the  inner  member  at  this  point  equals  twice  that 
of  the  outer  one,  it  follows,  since  the  action  should  be 
come  equal  upon  the  two  at  «,  that  £  of  the  whole 
thrust  of  the  rib  must  be  transferred  from  the  inner  to 
the  outer  member  between  c  and  a,  by  the  thrust  and 
pull  of  diagonals,  exerted  in  the  direction  of  the  normal 
curve  ;  the  action  accumulating  and  increasing  upon 
successive  diagonals  each  way  from  c,  and  in  like 
manner  from  k. 

The  action  of  diagonals  is  still  further  affected  by  the 
transfer  of  the  action  of  load,  from  the  outer  to  the  inner 
member ;  the  load  being  first  applied  directly  to  the  outer 
curved  member.  Hence  it  becomes  a  somewhat  com 
plicated  problem  to  determine  the  maximum  action 
of  diagonals ;  especially  as  the  complication  becomes 
increased  by  taking  into  account  the 

• 
EFFECTS  OF  TEMPERATURE. 

LXXVIIT.  The  expansion  and  contraction  of  metallic 
arches  without  chords,  the  ends  remaining  fixed  as  to 
position  and  distance  asunder,  must  obviously  cause 
the  intermediate  portions  to  rise  and  fall  with  -the 
increase  and  decrease  of  temperature. 

The  outer  and  inner  members,  if  parallel,  being 
similar  concentric  arcs,  will  rise  and  fall,  by  the  same 


EFFECTS  OF  TEMPERATURE.  127 

changes  of  temperature,  proportionally  to  their  respec 
tive  radii  ;*  the  outer  one  undergoing  the  greater  ver 
tical  change,  whence,  it  must  follow  that  in  warm 
weather  the  outer,  and  in  cold  weather  the  inner 
member  sustains  the  greater  relative  compression ,  a 
result  for  which  there  appears  to  be  no  obvious  remedy, 
except  by  balancing  the  end  bearings  upon  pivots  at  a 
and  k ;  which  would  allow  the  two  curved  members  to 
adjust  themselves  to  an  equal  action  upon  the  two. 
Or,  if  the  curves  be  formed  upon  the  same  radius,  and 
of  equal  length,  they  would  rise  and  fall  alike,  and  the 
distance  across  the  web  vertically,  would  be  the  same 
at  all  parts  of  the  arch. 

In  this  case,  as  in  all  others,  of  the  arched  rib,  the 
depression  of  the  arch,  whether  from  reduction  of  tem 
perature,  or  the  action  of  load,  would  be  attended  by 
increased  thrust  action,  or  diminished  tension  action 
upon  diagonals  less  inclined  from  the  vertical  position, 
and  the  reverse  of  action,  upon  those  more  inclined. 

The  absolute  rise  or  fall  of  an  arch,  resulting  from 
a  given  change  of  temperature,  may,  without  essential 
error,  be  regarded  as  proportional  to  the  change  in  the 
length  of  a  circular  arch  of  the  same  span  and  depth 
(from  chord  to  vertex),  within  the  limits  of  change 
produced  by  temperature ;  and,  may  be  found  by  the 
following  process  : 

Divide  the  square  of  the  half  chord  by  the  depth  of 
arch  (i?),  add  the  divisor  to  the  quotient,  and  half  the 
sum  equals  the  radius.  Divide  the  half-chord  by  the 
radius,  to  get  the  natural  sine  of  half  the  arc ;  find 
in  the  table  of  giatural  sines,  the  angle  corresponding 

*  The  curves  not  being  supposed  to  be  circular  arcs,  it  is  not  strictly 
correct  to  speak  of  their  radii,  but  the  meaning  will  be  comprehended. 


128  BRIDGE  BUILDING. 

with  the  sine  thus  found,  and  double  that  angle,  for 
the  number  of  degrees  in  the  arc.  Multiply  the  num 
ber  of  degrees  (reducing  minutes  and  seconds  to  the 
decimal  of  a  degree),  by  .01745329  (=  length  of  a  de 
gree,  radius  being  equal  to  1),  for  the  length  of  the  arc. 

Then,  in  the  same  manner,  find  the  length  of  an  arc 
upon  the  same  chord,  and  with  a  depth  (vr)  one  or  two 
per  cent  greater  or  less  than  v ;  and,  the  difference  in 
length  of  arcs  thus  found,  is  to  the  difference  between 
v  and  v',  as  the  change  in  length  of  arch  due  to  the 
given  change  of  temperature,  to  the  rise  or  fall  of  the 
arch,  resulting  from  such  change. 

By  applying  this  rule  to  a  specific  case,  we  can  the 
better  appreciate  the  importance  of  the  effects  of  change 
of  temperature  upon  this  species  of  arched  ribs.  If  we 
assume  an  arch  of  500  feet  chord  and  50  feet  depth,  =r, 
we  find  the  length  of  arc  to  be  513.25 //.  The  length  of 
an  arc  of  the  same  span,  and  a  depth  (vf)  =  51  /£.,  is 
513.715//.,  the  difference  being  0.465/if.  The  expan 
sion  of  steel  for  a  change  of  110°  Fahrenheit,  is 
.0007271  x  length  (513.25),  =  .37318.  We  have,  there 
fore,  .465  :  1ft.  :  :  .37318  :  .8025ft.  =  rise  or  fall  of  the 
arch  in  the  centre,  resulting  from  a  change  of  110°. 

Regarding  this  rise  in  the  centre  as  the  abscissa  of 
a  parabola,  and  the  half  chord  as  the  corresponding 
ordinate,  the  rise  at  any  other  point  of  the  curve  is 
equal  to  the  difference  between  .8025,  and  the  abscissa 
answering  to  the  ordinate  of  the  given  point 

Suppose  the  point  be  10  feet  from  the  end,  and  the 
ordinate,  of  course,  240/2.,  we  have,  2502 :  2402 : :  .8025 
:  .7395  =  abscissa  for  the  given  point ,  whence,  the 
rise  at  that  point,  equals  .8025— .7395  =  .063/if. 


EFFECTS  OF  TEMPERATURE. 


129 


Fio.  24. 


Let  Fig.  24  represent  the  end  portion  of  the  arch,  abe 
the  upper,  and  gc  the  lower  member,  ag  and  be  the 

width  of  web, =12'.  «6,  with  a 
horizontal  reach  of  10',  equals 
10.75'.  Then,  bg  being  re 
garded  as  '  a  rectangle,  the 
diagonal  ac=  16.1ft  and  the 
temperature  being  raisedllO0, 
the  points  b  and  c  rise  to  6'  and 
c',  66'  being  equal  to  the  ver 
tical  rise  multiplied  by  the 
cosine  of  the  angle  abd,  i.  e., 
equal  to  .062  X  cosine  abd. 
This  angle  is  a  little  over  22°,  and  its  cosine  about  .93 
whence  bb'**. 058ft,  =<?c'.  Joining  a  with  c',  and  draw 
ing  c'f  at  right  angles  with  ac,  and  acr  (as  these  lines 
are  essentially  parallel),  we  have  c/,=cc'x  sin.  acb=cc' 
x  — =. 038ft,  =•  the  contraction  required  to  take  place 
in  the  length  of  the  diagonal  ac,  to  accommodate  a 
shange  of  110°  in  temperature. 

In  the  mean  time  the  point  e  rises  to  e',  the  distance 
ee'  being  equal  to  .1147,  so  that  c'ef  is  extended  about 
the  same  as  ac'  is  contracted ;  a  change  equal  to  what 
would  be  produced  by  a  force  of  70,000  Bbs  to  the  square 
inch  of  cross  section. 

If  the  normal  length  of  the  diagonals  be  adjusted  for 
a  medium  temperature,  the  change  would  be  half  the 
above  amount  each  way,  or  equal  to  that  produced  by 
35,000  ft)s  to  the  inch. 

Succeeding  diagonals  toward  the  centre  would  be 
affected  in  a  similar  manner,  though  in  a  less  degree  ; 
and  the  consequence  must  be  an  accumulation  of  thrust 
or  compression  upon  the  inner  member  toward  the 
centre,  and  the  outer  one  toward  the  ends,  upon  a  rise 
17 


130  BRIDGE  BUILDING. 

of  temperature,  and  the  reverse  on  a  fall  below  the 
normal  point. 

THE  WIDTH  OF  WEB. 

LXXXIX.  For  an  arch  of  500  ft.  chord,  and  50  foot 
depth.  We  have  seen  that,  with  a  load  as  assumed 
[LXXIV],  with  reference  to  Fig.  22,  the  aggregate  aber 
ration  outward  and  inward,  traverses  a  zone  of  .162i?, 
equal  in  this  case,  to  .162  x  50  =  8.1  ft.  If  the  web, 
therefore,  be  8.1  feet  wide  between  centres  of  curved 
members,  the  equilibrated  curve  will  reach  the  centre 
of  said  members  at  the  points  ot  greatest  aberration, 
both  ways,  and  the  whole  thrust  at  these  points,  will  fall 
upon  a  single  member,  producing  as  we  have  already 
seen,  77  fa  per  cent  of  the  amount  of  thrust  due  to  a 
maximum  uniform  load  ;  being  over  55  per  cent  more 
stress  under  a  partial  than  under  a  full  load. 

Again,  suppose  the  web  to  be  12  feet  wide.  The 
distorted  curve  would  approach  within  two  feet  of  the 
outer  and  inner  curved  members,  throwing  upon  one 
member  at  one  point,  and  upon  the  opposite  member 
at  another  point,  almost  30  per  cent  more  action  than 
what  is  produced  by  the  full  maximum  load.  It  was 
shown  moreover  [LXXV]  that  nothing  short  of  .545r= 
.545x50=27.25  feet  width  of  web,  could  be  relied  on  to 
give  as  small  a  stress  upon  the  curved  members  in  this 
particular  case  of  a  partial,  as  that  produced  by  a  full 
maximum  load. 

This  would  be  an  inconvenient,  and  an  expensive 
width  of  web,  and  probably  a  less  width  would  be  pre 
ferable,  even  with  a  greater  occasional  stress  upon  the 
curved  members  which  might  be  enlarged  in  section 
in  parts  liable  to  the  greater  stress.  But  I  shall  not 
undertake  at  this  time,  to  determine  the  exact  optimum. 


BRIDGE  MATERIALS.  131 

Finally,  considering  the  difficulty  of  securing  the 
most  efficient  thrust  action  of  the  curved  members  of 
the  arch,  the  serious  disturbances  as  to  the  action  of 
the  diagonals  composing  the  web  system,  occasioned 
by  changes  of  the  temperature,  together  with  the  extra 
weight  and  strength  of  piers  and  abutments  to  with 
stand  the  horizontal  thrust  of  the  arches,  it  seems  rea 
sonable  to  conclude  that  the  erect  metallic  arch  bridge 
will  only  be  adopted  under  rare  and  peculiar  circum 
stances  ;  and  that  in  such  cases,  the  plans  should  be 
subjected  to  especial  examination  and  investigation. 

Truss  bridges  possess  the  advantage  of  having  all 
the  forces  in  operation,  except  the  vertical  action  of 
weight,  and  the  opposite  resistance  of  the  end  supports 
resisted  by  means  of  members  contained  within  the 
structures  themselves,  and  composed  of  materials  of  so 
nearly  uniform  expansibility  by  heat,  that  no  important 
disturbance  in  the  relations  of  the  different  members, 
can  be  produced  by  changes  of  temperature.  Plans, 
also,  may  be  so  arranged  as  to  secure  a  near  approxi 
mation  to  uniform  maximum  stress  upon  all  the  parts ; 
at  least,  to  a  much  greater  degree  than  seems  practica 
ble  in  the  case  of  the  arch  without  chords. 


132  BRIDGE  BUILDING. 


BRIDGE  MATERIALS. 

LXXX.  Having  discussed  the  general  principles 
and  relative  characters  and  merits  of  different  plans 
and  forms  of  bridge  trusses,  and  their  proper  propor 
tions,  particular  and  general,  the  question  as  to  the 
best  materials  for  the  purposes  of  bridge  construction 
may  properly  be  considered. 

We  have  seen  that  the  materials  of  a  bridge  truss 
are  principally  subjected  to  two  kinds  of  action,  that 
of  tension,  and  that  of  compression.  Lateral,  or  trans 
verse  action  should  be  avoided  in  the  principal  parts 
and  members  of  the  truss. 

It  is  obvious  then,  that  those  materials  best  calcu 
lated  to  resist  these  kinds  of  force  respectively,  should, 
when  practicable  without  sacrifice  of  economy,  be  em 
ployed  in  the  situations  where  those  forces  are  respect 
ively  exerted.  For  instance,  when  the  diagonals  act 
by  tension,  the  upper  chord  (or  the  arch,  in  case  of 
the  arch  truss),  and  the  verticals,  should  be  composed 
of  the  material  best  adapted  to  the  sustaining  of  a  com- 
pressive  force,  while  the  lower  chord  and  the  diagonals, 
should  be  of  the.best  material  for  sustaining  tension. 

"Wood  and  iron  are  the  only  materials  that  have  been 
employed  in  the  construction  of  bridge  superstructures 
to  an  extent  worthy  of  notice ;  and  it  seems  reasonable  to 
conclude  that  on  these  we  must  place  our  dependence. 

Cast  iron  resists  a  greater  compressive  force  than 
any  other  substance  whose  cost  will  admit  of  its  being 
used  as  a  building  material.  Steel  has  a  greater  power 
of  resistance,  but  its  cost  precludes  its  employment  as 


BRIDGE  MATERIALS.  133 

a  material  for  building  purposes.*  Wrought  iron  re 
sists  compression  nearly  equally  with  cast  iron.  But 
its  cost  is  twice  as  great,  which  gives  the  cast  iron  a 
decided  advantage. 

On  the  other  hand,  wrought  iron  resists  a  tensile  force 
nearly  four  times  as  well  as  cast  iron,  and  12  or  15 
times  as  well  as  wood,  bulk  for  bulk. 

Not  only  are  these  the  strongest  materials,  but  they 
are  also  the  most  durable.  In  fact,  with  proper  pre 
cautions,  they  may  be  regarded  as  almost  imperishable. 

It  would  seem  then,  that  wrought  iron  for  tension, 
and  cast  iron  for  compression,  were  the  best  materials 
that  could  be  employed  in  building  bridges.  But 
wood,  though  greatly  inferior  in  strength  and  dura 
bility,  is  much  cheaper  and  lighter,  so  that,  making  up 
with  quantity  for  want  of  strength,  and  by  frequent  re 
newals,  its  want  of  durability,  it  has  hitherto  been 
almost  universally  used  in  this  country  for  bridge 
building;  and,  in  the  scarcity  of  mezns,  and  the  un 
settled  state  of  things  in  anew  country,  where  improve 
ments  are  necessarily,  to  a  great  extent,  of  a  temporary 
character,  this  is  undoubtedly  the  most  economical 
material  for  the  purpose. 

But  it  is  believed  that  the  state  of  things  has  now 
assumed  that  degree  of  settled  permanency  in  many 
parts  of  this  country,  and  available  means  have  accu 
mulated  to  that  extent  which  renders  it  consistent  with 
true  economy  to  give  a  character  of  greater  permanence 
to  our  improvements ;  and,  in  the  erection  of  import 
ant  works,  to  have  more  reference  to  durability,  even 
at  the  cost  of  a  greater  present  outlay.  In  this  view 

*  This  remark,  made  originally  some  twenty-five  years  ago,  may  re 
quire  some  modification  at  the  present  time,  when  steel  is  being  em 
ployed  extensively  for  rail  way  track,  and  in  some  important  arch  and 
suspension  bridges  ;  but  not  in  truss  bridges,  to  the  writer's  knowledge. 


134  BRIDGE  BUILDING. 

of  the  subject,  it  seems  highly  probable  that  one  of  the 
channels  in  which  this  tendency  of  things  will  develop 
itself,  will  be  in  the  extensive  employment  of  iron  in 
the  construction  of  important  bridges.  With  this  im 
pression,  I  proceed  to  some  general  comparisons  as  to 
the  relative  cost  and  economy  of  wood  and  iron  as 
materials  for  bridges. 

LXXXI.  The  power  of  cast  iron  to  resist  compres 
sion,  equals  some  twenty  times  that  of  wood ;  conse 
quently,  it  will  only  require  one  twentieth  as  much  of 
the  former  to  withstand  a  given  force,  provided  it  can 
be  put  into  a  form  in  which  its  liability  to  flexure,  and 
yielding  laterally,  is  not  greater  than  that  of  wood. 
This  may  be  accomplished  in  part,  by  giving  the  iron 
a  hollow  form,  so  as  to  make  the  diameter  of  the  pieces 
approximate  to  an  equality  with  twenty  times  the  same 
amount  of  wood,  which  must  generally  be  used  in  a 
simple  rectangular,  or  cylindrical  form  of  section. 

Assuming,  then,  that  a  cubic  foot  of  cast  iron  will 
do  the  same  work  as  15  cubic  feet  of  wood  (after  mak 
ing  allowance  for  the  necessarily  smaller  diameter  of 
the  iron),  we  can  institute  a  comparison  which  would 
seem,  upon  the  surface,  to  show  the  relative  economy 
of  the  two  materials. 

A  cubic  foot  of  cast  iron,  manufactured  for  the  work 
will  cost  about  $13.00.  15  cubic  feet  of  wood  in  abridge 
will  cost,  say  $6.00.  Whence  it  appears  that  the  cast 
iron  is  more  than  twice  as  expensive,  in  the  first  outlay, 
for  sustaining  a  compressive  force,  as  wood. 

Again  a  cubic  foot  of  wrought  iron  in  the  work,  say 
450  ft>  at  7  Jets.  =$34.00. 

Wood  is  about  ^  as  strong  as  iron.  But  about  one- 
half  of  its  fibres  must  be  separated  in  order  that  the 


BRIDGE  MATERIALS.  135 

other  half  may  be  so  connected  in  the  structure,  as  to 
be  available  to  their  full  strength,  acting  by  tension. 
Hence,  it  will  take  some  30  feet  to  equal  one  of  iron ; 
for  which  it  will  cost,  say  $12;  showing  a  difference  of 
a  little  less  than  three  to  one  ;  making  the  average  for 
both  kinds  of  iron,  reckoning  equal  quantities  of  each, 
about  2.6  to  1. 

To  offset  against  this,  we  have  the  superior  durability 
of  the  iron,  which,  as  before  observed,  may  be  regarded 
as  imperishable ;  whereas,  wood  requires  frequent  re 
newals,  at  a  cost  each  time,  equal  to  the  iirst  outlay. 
Now,  the  first  cost  of  the  iron  is  sufficient  to  provide 
for  the  first  cost  of  the  wood,  and  nearly  two  renewals. 
Besides  this,  money,  though  an  inanimate  substance, 
is,  nevertheless,  in  these  usurious  times,  made  t<>  1  e 
exceedingly  prolific  ;  insomuch,  that  with  good  man 
agement,  it  is  found  to  double  itself  once  in  ten  or 
twelve  years,  according  to  the  hardness  of  face  in  the 
lender,  or  of  fortune  in  the  borrower. 

Assuming  5  per  cent  per  annum  as  the  net  income 
of  money  invested,  the  term  of  time  in  which  the  1  ffc 
dollars  saved  in  the  wooden  structure,  will  require  to 
produce,one  dollar  for  renewal,  will  show  the  time  that 
wood  ought  to  last,  to  be  equal  with  iron  in  economy, 

One  dollar  and  sixty  cents  at  compound  interest  will 
yield,  at  5  per  cent,  one  dollar  in  a  little  less  than  ten 
years.  Therefore,  if  an  imperishable  iron  structure 
cost  2.6  times  as  much  as  one  of  wood,  and  the  latter 
last  but  ten  years,  and  money  will  net  5  per  cent,  com 
pound  interest,  the  two  materials  are  nearly  upon  a  par 
as  to  economy. 

Experience  has  shown  that  wooden  bridges,  unpro 
tected  by  roofing  and  siding,  seldom  last  with  safety 
over  eight  years,  or  thereabouts ;  and,  the  more  there 


136  BRIDGE  BUILDING. 

be  expended  to  increase  the  durability,  the  less  surplus 
capital  will  be  left  to  be  invested  toward  renewals. 

LXXXII.  But  the  above  comparison  is  too  super 
ficial  and  general  to  be  entitled  to  a  great  deal  of  con 
fidence,  except,  perhaps,  as  it  regards  the  sustaining 
of  a  given  weight  by  a  simple  post,  or  suspending  it  by 
a  bar  or  rod  of  iron  or  wood.  In  the  complicated  as 
semblage  of  pieces  forming  the  superstructure  of  a 
bridge,  there  are  numerous  other  facts  and  considera 
tions  which  materially  vary  the  results.  First,  there 
is  a  difficulty  in  connecting  pieces  of  timber  in  such  a 
manner  that  every  part  may  be  proportioned  to  the 
strength  required  of  it,  to  the  same  extent  as  can  be 
done  with  iron.  Second,  it  is  frequently  necessary  to 
use  considerable  quantities  of  iron  in  bolts  and  fastenings 
for  putting  together  a  structure  of  wood  requiring  great 
stability.  Third,  wood  soon  loses  a  portion  of  its 
strength  by  partial  decay,  and  consequently,  requires 
additional  strength  in  the  beginning,  that  it  may  be 
safe  for  a  time  after  decay  has  commenced. 

Hence,  but  little  can  be  predicated  upon  the  simple 
general  comparison  of  wood  and  iron  as  to  strength 
and  cost,  relative  to  the  comparative  economy  of  the 
two  materials  for  bridge  building. 

It  is  only  by  comparing  the  results  of  actual  experi 
ence,  or,  where  this  has  not  been  had,  by  comparing 
the  results  of  detailed  estimates,  upon  well  matured 
plans,  founded  on  well  established  principles,  that  a 
satisfactory  conclusion  can  be  arrived  at. 

With  regard  to  wooden  bridges,  much  experience  has 
been  had,  and  the  reasonable  presumption  is,  that  a  good 
degree  of  economy  has  been  attained  in  their  construc 
tion.  But  the  idea  of  building  iron  bridges  in  this 


BRIDGE  MATERIALS.  137 

country,  is  of  recent  date,  and  but  little  has  been  experi 
mentally  proved  in  relation,  to  their  cost  and  qualities. 

LXXXIII.  This  much,  however,  my  own  experience 
has  demonstrated.  Having  received  Letters  Patent  for 
an  "  Iron  Truss  Bridge,"  upon  the  arch  truss  plan,  and 
constructed  two  bridges  thereon,  over  the  Enlarged 
Erie  Canal  (of  72  and  80  feet  spans),  one  of  which  has 
been  in  use  for  six  years,  it  may  be  regarded  as  a  de 
monstrated  fact,  that  bridges  may  be  sustained  by 
iron  trusses.  It  has  also  been  shown  that  the  cost  of 
the  above  class  of  bridges,  is  only  about  25  per  cent 
more  than  the  same  class  of  bridges  of  wood,  as  hereto 
fore  built,  under  the  most  favorable  circumstances,  upon 
the  Erie  Canal.  That  the  iron  portion,  constituting 
some  three-fourths  of  the  whole,  as  regards  expense, 
in  the  iron  bridge,  gives  fair  promise  of  enduring  for 
ages,  while  the  wooden  structure  can  only  be  relied  on 
to  last  eight  or  ten  years. 

Upon  these  facts,  experimentally  established,  I  found 
the  following  comparison  : 

A  common  road  bridge  of  72/£.  span  (the  usual 
length  for  the  enlarged  Erie  Canal),  will  cost,  with 
iron  trusses  : 

For  7,000  ibs.  of  cast  iron  at  Sets., $210. 

"    6,000  "    "  wrought  iron,  manufactured 

for  the  work,  at  7cts.,  420. 

"    Timber,  labor  and  painting, 230. 

"    Superintendence  and  profit, 80. 

"Whole  first  cost, $940. 

$175  will  renew  the  perishable  part  once  in 
9  years,  to  produce  which,  at  5  per  cent 
compound  interest  will  require  capital  of,  320. 

Total  for  a  perpetual  maintenance,  $1,260. 
18 


138  BRIDGE  BUILDING. 

"With  wooden    trusses,  fastened    with    iron 

for  timber,  labor,  paint  and  profit,      $550 
"     2,000  Sbs.  of  iron  fastenings, 150. 

Whole  first  cost, §700. 

(Some  have  cost  §1000,  or  §12,000,  and  taken 

3  to  4  thousand  pounds  of  iron) 

To  renew  $550  worth  of  perishable  material 

once  in  9  years,  will  require,  at  5  per 

cent,  compound  interest, §1,000. 

Total  for  perpetual  maintenance, §1,700. 

The  reason  of  the  apparent  difference  between  this 
result,  and  that  arrived  at  from  the  general  comparison 
of  the  cost,  &c.,  of  wood  and  iron,  is,  that  the  bridges 
here  referred  to,  have  been  constructed  with  a  very 
large  amount  of  iron  fastenings,  and  with  large  quanti 
ties  of  casing  and  painting  for  protection  and  appear 
ance.  Were  the  comparison  confined  strictly  to  the 
expense  of  timber  work,  in  the  sustaining  parts  of  the 
trusses,  the  result  would  be  found  not  to  differ  so  es 
sentially  from  that  of  the  general  comparison. 

The  above  estimate  of  §700,  for  the  first  cost  of  a 
72  foot  wooden  bridge,  though  considerably  below  the 
average  cost  of  canal  bridges  of  that  description,  is 
nevertheless  believed  to  be  greatly  above  the  minimum 
for  which  bridges  may  be  built,  dispensing  with  the 
parts  which  are  not  essential  to  strength. 

It  is  probable  that  bridges  may  be  built  for  §500,  as 
about  the  minimum,  of  equal  strength  and  convenience, 
and  nearly  the  same  durability,  as  those  hitherto  built 
upon  the  Erie  Canal  Enlargement  at  a  cost  of  from 
800  to  1,000  dollars.  Upon  this  supposition,  which 
may  be  regarded  as  an  extreme  case  in  favor  of  wood, 
the  comparison  will  stand  thus  : 


BRIDGE  MATERIALS.  139 

First  cost  of  wooden,  structure, $500 

Capital  invested  at  5  per  cent  to  produce  $500 

once  in  9  years  for  renewal, 909 

Total  for  perpetual  maintenance, $1409 

The  same  for  iron  structure,  as  above, 1260 

Balance  in  favor  of  the  iron  bridge, $149 

Finally,  since  theoretical  calculation  and  general 
comparison  show  a  probable  advantage,  for  a  long  term 
of  time,  and  experience,  as  far  as  it  has  gone,  shows  a 
decided  advantage  in  favor  of  iron,  it  would  seem  very 
unwise  to  discard  the  latter,  without  at  least  a  fair 
trial  of  its  merits.  If  in  the  first  essays  at  iron  bridge 
building,  the  iron  bridge  has  competed  so  successfully 
with  wooden  bridges,  improved  by  the  experience  of 
ages,  may  not  the  most  satisfactory  results  be  antici 
pated  from  an  equal  degree  of  experience  in  the  con 
struction  and  use  of  iron  bridges  ? 

LXXXIV.  Presuming  the  affirmative  to  be  the 
only  rational  answer  to  the  above  question,  I  have  ar 
ranged  the  details  of  plans  for  carrying  into  practice 
the  preceding  principles  and  suggestions  in  the  con 
struction  of  rail  road  bridges  of  iron. 

I  have  also  made  careful  detailed  estimates  of  the 
expense  of  bridges  of  different  dimensions  and  in  dif 
ferent  circumstances,  some  of  the  more  general  results 
of  which  I  will  here  state. 

In  proportioning  the  parts  of  a  rail  road  bridge,  1 
have  assumed  that  it  may  be  exposed  to  a  load  of  2,000ft>s. 
per  foot  run,  for  the  whole,  or  any  part  of  its  length,  in 
addition  to  its  own  weight;  and  in  case  of  tension,  have 
allowed  one  square  inch  cross  section  of  wrought  iron 
for  every  10,000  ft>s.  of  the  maximum  strain  produced 


140  BRIDGE  BUILDING. 

upon  every  part  by  such  weights,  acting  by  dead  pres 
sure.  In  case  of  thrust,  or  crushing  force,  I  have  al 
lowed  one  square  inch  cross  section  of  cast  iron,  for 
every  12,OOOSbs.  acting  on  pieces  (mostly  in  the  form  oi 
hollow  cylinders),  of  a  length  equal  to  18  diameters, 
and  a  greater  amount  of  material,  where  the  ratio  of 
length  to  diameter  is  greater;  always  having  regard 
to  practicability,  as  well  as  theoretical  proportions,  in 
adjusting  the  dimensions  of  the  part. 

My  estimates,  made  upon  these  bases,  have  fully  sa 
tisfied  me  that  a  bridge  of  100  feet  span,  with  track 
upon  the  top  (with  wooden  cross-beams),  will  cost  about 
$2,000,  or  $20  per  foot,  assuming  the  present  prices 
of  iron  (1846),  in  ordinary  circumstances.  If  the  track 
pass  near  the  bottom  of  the  trusses,  the  expense  will  be 
increased  by  two  or  three  dollars  a  foot. 

For  a  span  of  140  feet,  by  a  liberal  detailed  estimate 
I  make,  in  round  numbers,  a  cost  of  §4,000.  For  70 
feet,  I  estimate  a  cost  of  9  to  10  hundred  dollars,  ac 
cording  to  circumstances. 

Thus  it  will  be  seen  that  actual  estimate  makes  the 
cost  of  a  single  stretch  of  any  length,  very  nearly  as 
the  square  of  the  length,  as  should  be  expected  from 
the  nature  of  the  case.  Hence,  knowing  the  cost  of  a 
span  of  any  given  length,  we  readily  deduce  that  of  a 
span  of  any  other  length,  in  similar  circumstances,  with 
reliable  certainty. 

Now,  although  my  investigations  have  forced  the 
conviction  upon  me,  that  where  strong  and  durable 
bridges  are  required,  iron  should  be  preferred  in  their 
construction,  still  there  is  a  multitude  of  cases  where 
wooden  structures  should  be  preferred ;  especially  in 
sections  of  country  comparatively  new,  where  timber  is 


PRACTICAL  DETAILS.  141 

plenty  and  capital  scarce ;  and  where  improvements 
must  necessarily  be  of  a  more  temporary  character. 

With  this  view  of  the  subject,  I  have  given  consi 
derable  attention  to  the  details  of  wooden  bridges ;  and, 
with  a  good  deal  of  invest.gation  and  experiment,  have 
arranged  plans  which  are  confidently  believed  to  pos 
sess  important  advantages  over  the  plans  generally  in 
use. 

The  preceding  few  pages  have  been  transcribed  from 
the  author's  original  and  first  essay  upon  bridge  build 
ing;  and  are  introduced  here,  not  on  account  of  any 
practical  value  they  may  possess  in  the  present  state  of 
progress  in  the  science  of  bridge  construction.  But 
they  may  possess  some  little  interest  as  marking  about 
the  starting  point  of  the  construction  and  use  of  Iron 
Truss  Bridges. 

If  the  estimates  above  exhibited,  of  the  cost  of  iron 
bridges,  appear  small  and  inadequate,  under  the  lights 
furnished  by  the  experience  of  a  quarter  of  a  century, 
much  allowance  may  be  claimed  on  account  of  the 
change  of  times  and  circumstances  within  the  period  in 
question.  And,  when  it  is  borne  in  mind  that  the 
author  actually  contracted  for,  and  built  iron  railroad 
bridges  of  40  and  50  feet  span,  for  $10,  and  of  146  feet 
for  $30  per  foot,  the  estimates  above  given  may  not 
seem  entirely  preposterous,  although  much  higher 
prices  are  obtained  for  bridges  of  like  dimensions  at 
the  present  day. 


PRACTICAL  DETAILS. 

LXXXY.  In  preceding  pages  I  have  endeavored  to 
give  a  short  and  comprehensive  general  view  of  the 


142  BRIDGE  BUILDING. 

subject,  and  to  ascertain  and  point  out  the  best  general 
plans  and  proportions,  for  the  main  longitudinal  trusses, 
or  side  frames  of  bridges,  and  the  relative  stresses  ol 
their  several  parts. 

The  side  trusses  may  be  regarded  as  vastly  the  most 
important  parts  of  the  structure,  and  the  strength  and 
sufficiency  of  these  being  secured,  there  is  much  less 
difficulty  in  arranging  the  remaining  parts,  the  forces 
to  which  they  are  exposed  being  much  less  than  those 
acting  upon  the  trusses.  I  propose  now  to  enter  more 
into  details,  and  give  such  practical  explanations  and 
specifications  as  to  the  strength  of  materials,  the 
methods  of  connecting  the  several  parts  or  pieces,  both 
in  the  main  trusses,  and  other  parts  of  the  structure, 
illustrated  by  the  necessary  plans  and  diagrams,  as,  it 
is  hoped,  will  enable  the  young  engineer  and  practi 
cal  builder  to  proceed  with  judgment  and  confidence 
in  this  important  branch  of  the  profession. 


IRON  BRIDGES. 
STRENGTH  OF  IRON. 

LXXXVI.  Iron  has  the  power  of  resisting  mechani 
cal  forces  in  several  different  ways.  It  may  resist  forces 
that  tend  to  stretch  it  asunder,  or  forces  which  tend  to 
compress  and  crush  it;  the  former  producing  what  is 
sometimes  called  a  positive,  and  the  latter,  a  negative 
strain.  It  may  also  be  exposed  to,  and  resist  forces 
tending  to  produce  rupture  by  extending  one  side  of 
the  piece,  and  compressing  the  opposite  side  ;  as  where 
a  bar  of  iron  supported  at  the  ends,  is  made  to  sustain 
a  weight  in  the  middle,  which  tends  to  stretch  the 


IRON  BRIDGES.  143 

lower,  and  compress  the  upper  part.  This  is  called  a 
lateral,  or  transverse  strain. 

Iron  may  likewise  be  acted  upon  by  forces  tending 
to  force  it  asunder  laterally,  in  the  manner  of  the  ac 
tion  of  a  pair  of  shears.  This  is  called  a  shear  strain  ; 
and  though  less  important  than  either  of  the  preced 
ing  cases,  it  will  frequently  have  place  in  bridge  work, 
partially  at  least,  in  the  action  of  rivets,  and  connect 
ing  pins. 

With  regard  to  the  simple  positive  and  negative 
strength  of  iron  it  is  only  necessary  for  me  to  state  in 
this  place,  as  the  result  of  a  multitude  of  experiments, 
that  a  bar  of  good  wrought  iron  one  inch  square,  will 
sustain  a  positive  strain  of  about  60,0001fos.  on  the 
average  ;  and  a  negative  strain,  in  pieces  not  exceeding 
about  twice  the  least  diameter,  of  70  or  80  thousand 
pounds.  But  in  both  cases,  the  metal  yields  perma 
nently  with  much  less  stress  than  the  amounts  here 
indicated  ;  and  hence,  as  well  as  for  other  considera 
tions,  it  can  never  be  safely  exposed  in  practice,  to 
more  than  a  small  proportion  of  these  stresses,  say 
from  |  to  J. 

Cast  iron  resists  apositive  strain  of  15,000  to  30,000fbs. 
to  the  square  inch,  but  usually,  not  over  18,000.  But 
it  is  seldom  relied  on  to  sustain  this  kind  of  action  es 
pecially  in  bridge  work,  wrought  iron  being  much  bet 
ter  adapted  to  the  purpose.  On  rare  occasions,  it  may 
perhaps  safely  be  exposed  to  a  strain  of  3,000  to4,000ft>s. 
to  the  square  inch,  but  should  not  be  used  under  ten 
sion  strain,  when  wrought  iron  can  be  conveniently 
substituted. 

Cast  iron,  however,  is  capable  of  resisting  a  much 
greater  negative  strain  than  wrought  iron ;  its  power 
of  resistance  in  this  respect,  being  from  80,000  to 


144  BRIDGE  BUILDING. 

140,000ft>s. ;  seldom  less  than  100.000  to  the  square 
inch,  in  pieces  not  exceeding  in  length,  twice  the  least 
diameter. 

But  in  pieces  of  such  dimensions  as  must  frequently 
be  employed  in  bridge  work,  fracture  would  take  place 
by  lateral  deflection,  under  a  much  smaller  force  than 
what  would  crush  the  material.  It  is  therefore  neces 
sary  to  take  into  account  the  length  and  diameter,  as 
well  as  the  cross-section,  in  order  to  determine  the 
amount  of  compression  which  a  piece  of  cast  iron,  or 
any  other  material  may  be  relied  on  to  sustain. 

LXXXVII.  The  cause  of  lateral  deflection  resulting 
from  forces  applied  at  the  ends,  and  tending  to  crush 
a  long  piece  in  the  direction  of  its  length,  is  supposed 
to  be  a  want  of  uniformity  in  the  material,  and  a  want 
of  such  an  adjust  of  the  forces  that  the  line  joining  the 
centres  of  pressure  at  the  two  ends,  may  pass  through 
the  centre  of  resistance  in  all  parts  of  the  piece. 

These  elements  are  liable  to  considerable  variation, 
and  can  not  be  very  closely  estimated  in  any  case. 
Therefore  the  absolute  power  of  resistance  for  a  piece 
of  considerable  length,  can  not  be  deduced  by  calcula 
tion  from  the  simple  positive  and  negative  strength  of 
the  material,  but  resort  must  be  had  to  direct  experi 
ment  upon  the  subject ;  and,  even  wide  discrepancies 
should  naturally  be  expected  in  the  results  of  experi 
ment,  unless  the  lengths  of  pieces  experimented  upon, 
be  very  considerable. 

In  respect  to  pieces,  however,  having  their  lengths 
equal  to  twenty  or  more  times  their  diameters,  a  some, 
what  remarkable  degree  of  uniformity  is  found  in  their 
powers  of  negative  resistance,  and  the  following  for 
mula,  deduced  theoretically,  though  not  fully  sustained 


IRON  BRIDGES.  145 

by  experiment,  may  be  useful  in  determining  approxi 
mately  the  relative  powers  for  pieces  of  similar  cross- 
Bections,  but  different  dimensions.  The  power  of 
resistance  (R),  is  as  the  cube  of  the  diameter  (d)9  directly 
and  as  the  square  of  the  length  (I),  inversely,  that  is, 
R  is  as  -^. 

The  reason  of  this  formula  may  be  illustrated  with 
reference  to  Fig.  25,  in  which  adb  represents  a  post 
loaded  at  a,  so  as  to  bend  it  into  a  curve,  of  the  half 
of  which  cd  is  the  versed  sine.  It  is  obvious  that  in 
this  condition,  the  convex  side  of  the  post  is  exposed 
to  tension  (or  at  least,  to  less  compression  YIG.  25. 
than  the  other  side),  and  the  concave  side 
to  compression  ;  also,  that  the  effect  of  the 
load  at  a,  toward  breaking  the  post  at  d, 
is  as  the  versed  sine  cd,  which  is  as  the 
square  of  ab.  But  the  power  of  the  post 
to  resist  rupture  transversely,  is  manifestly  ^ 
as  the  cross-section  of  the  post  (i.  e.,  as  .the 
square  of  the  diameter),  multiplied  by  the 
diameter.  Hence,  the  power  is  as  the 
cube  of  the  diameter.  Now,  the  ability  of 
the  post  to  sustain  the  load  at  a,  is  directly 
as  the  power  to  resist  rupture,  just  determined,  and 
inversely  as  the  mechanical  advantage  with  which  the 
load  acts,  above  seen  to  be  as  the  square  of  the  length 
of  the  post.  Hence,  the  formula. 

We  shall  see  as  we  progress,  the  relation  which  this 
formula  seems  to  bear  to  the  results  of  experiment. 

The  following  list  of  experiments  made  by  the  author 
some  25  years  ago,  though  few  in  number,  and  upon 
a  somewhat  diminutive  scale,  nevertheless,  may  afford 
some  light  as  to  the  law  governing  the  resisting  power 
of  cast  iron  in  pieces  of  different  lengths,  as  compared 
19 


146 


BRIDGE  BUILDING. 


with  their  diameters.  It  may  at  least  enable  us  the 
better  to  appreciate  the  better  lights  since  shed  upon 
the  subject. 


LXXXYIII.    EXPERIMENTS    UPON    THE 
STRENGTH  OP  CAST  IRON,  IN  LONG  PIECES. 

Ends,  flat  cones  or  pyramids. 


NEGATIVE 


JL 

Form 

Inches. 

02 

G 

g 

£ 

of 

rZ 

.S 

9, 

a 

Remarks. 

c 

section. 

a 

J~ 

^ 

gj 

5 

si 

s 

^ 

^ 

1 

1 

Cylinder 

is 

9. 

016 

990 

1002 

Broke  TVn.  from  centre. 

2 

" 

M 

" 

978 

990 

Broke  ^  in.  from  centre. 

8 

Square 

i 

4< 

0.15 

803 

854 

Deflected  cornerwise,   and   flew 

out  without  breaking. 

4 

" 

" 

" 

« 

914 

938 

Broke    in   half    a    minute    not 

cornerwise,  £  inch  from  centre. 

5 

Cylinder 

A 

7.1 

0.126 

1417 

1437 

Broke  in  3  seconds,  ^  in.  from 

centre. 

6 

M 

•« 

<• 

u 

1377 

1397 

Broke  ||  in.  from  centre. 

•« 

" 

" 

" 

" 

Piece    flattened    by    flask    not 

shutting   true,   and  had    been 

straightened  with  the  hammer 

where  it  broke. 

7 

« 

»< 

4.5 

2580 

2580 

Broke  in  1  minute  into  4  pieces 

of  nearly  equal  lengths. 

Piece  of  same  as  last  experiment. 

8 

" 

" 

4.5 

3218 

3218 

Broke  in  \  minute  into  3  pieces 

in  centre,  and  1  in.  from  centre. 

9 

Square 

± 

4.5 

2813 

2838 

Broke  in  £  minute,  y^  in.  from 

centre,  deflected  parallel   with 

sides. 

From  experiments  7  and  8,  in  the  above  table,  it 
appears  that  cast  iron  will  sustain  at  the  extreme,  in 
cylindrical  pieces  whose  lengths  equal  about  14J  dia 
meters,  a  negative  strain  of  41,000  to  51,000fbs  to  the 
square  inch,  say  an  average  of  46,000.  Square  bars, 
according  to  experiment  9,  length  equal  to  18  diame 
ters  (or  widths  of  side),  will  sustain  about  45,000ft>s  to 
the  square  inch. 


IRON  BRIDGES.  147 

Now,  a  hollow  cylinder  of  a  thickness  not  exceeding 
about  Jy  of  the  diameter,  according  to  calculation,  has 
a  stiffness  transversely,  about  50  per  cent  greater  to  the 
square  inch  than  a  solid  square  bar  whose  side  equals 
in  width  the  diameter  of  the  cylinder.  Hence,  a  hollow 
cylinder  of  a  length  equal  to  18  times  its  diameter, 
should  sustain  a  negative  strain  of  67,500  fts.  to  the 
square  inch.  But  it  should  be  observed,  however,  that 
direct  experiments  upon  the  transverse  strength  of  the 
pieces  used  in  the  experiments  leading  to  the  results 
and  conclusions  above  stated,  as  to  negative  strength, 
showed  themto  possess  uncommon  strength  transversely, 
even  to  from  30  to  50  per  cent  greater  than  the  fair 
average  transverse  strength  of  cast  iron ;  as  will  be  seen 
hereafter.  It  is  therefore  not  considered  proper  to  es 
timate  the  strength  of  hollow  cylinders  of  the  propor 
tions  above  stated  at  more  than  45,000  or  46,OOOIbs.  to 
the  square  inch. 

The  hollow  cylinder  is  undoubtedly  the  form  best 
adapted  to  the  sustaining  of  a  negative  strain,  having 
equal  stiffness  in  all  directions.  It  is  therefore  highly 
desirable  that  the  power  of  that  form  of  pieces  to  resist 
compression,  with  different  lengths,  should  be  ascer 
tained  by  a  careful  and  extensive  series  of  experiments. 
But  until  that  shall  have  been  done,  and  the  results 
made  known,  I  shall  assume  the  above  estimate  upon 
the  subject,  as  probably  not  very  far  from  the  truth  ; 
subject,  however,  to  correction,  whenever  the  facts  and 
evidences  shall  be  obtained,  upon  which  the  correction 
can  be  founded.* 

In  the  mean  time,  since  we  know*  not  the  exact  ratio 
between  the  greatest  safe  practical  stress,  and  the  ab- 

*  Since  the  original  writing  of  this  paragraph  (25  years  ago),  exten- 
tensive  experiments  and  investigations  have  been  made,  in  the  direction 


148  BRIDGE  BUILDING. 

solute  strength  of  iron,  and  therefore  should  in  practice 
keep  considerably  within  the  limits  of  probable  safety, 
it  becomes  a  matter  of  less  importance  to  know  the 
exact  absolute  strength;  though  this,  of  course,  is  de- 
sirable. 

LXXXIX.  Having  decided  upon  a  measure  of 
strength  for  pieces  of  a  given  length,  we  may  properly 
endeavor  to  ascertain  the  rate  of  variation  for  different 
lengths  as  compared  with  the  diameters. 

It  is  seen  in  the  table,  [LXXXVIII]  that  two  cylindri 
cal  pieces  of  9  inches  in  length,  bore  the  one  990,  and 
the  other  9781bs.,  giving  a  mean  of  984  pounds. 

Now,  by  the  formula  -^,  the  same  cylinders  reduced 
to  4.5  inches,  should  sustain  four  times  as  much,  or 
3936ft>s.  But,  by  experiments  7  and  8,  we  find  that 
they  bore  only  2,580,  and  3,218,  a  mean  of  2,899 
pounds.  Whence  it  appears  that,  the  diameter  being 
the  same,  the  strength  diminishes  faster  than  the  length 
increases,  but  not  so  fast  as  the  square  of  the  length 
increases  ;  being  about  half  way  between  the  two.  In 
fact,  if  we  examine  the  results  of  these  experiments 
throughout,  we  find  that  the  weights  borne  by  pieces 
of  like  cross-sections,  whether  round  or  square,  were 
very  nearly  the  arithmetical  mean  between  the  results 
obtained  by  considering  them  to  be  inversely  as  the 
simple  length,  and  as  the  square  of  the  length,  succes 
sively. 

For  illustration  ;  take  experiments  1  and  5.  If  the 
piece  9  inches  long  bore  990  ft>s.,  taking  the  strength 

here  indicated,  and  ingenious  and  convenient  formulae  deduced  upon 
the  subject  involved,  which  might  perhaps,  be  profitably  substituted 
for  the  writer's  own  crude  deductions  in  this  behalf.  But,  as  previously 
remarked  on  other  occasions,  the  latter  may  possess  interest  as  affording 
a  monument  upon  the  line  of  the  march  of  progress. 


IRON  BRIDGES.  149 

to  be  inversely  as  the  length,  we  have  this  proportion 
i  :  ~ : :  990  : 1,255.  Then,  taking  the  strength  to  be 
inversely  as  the  square  of  the  length,  we  have  :  1- :  ^i_ 
: :  990  :  1,591.  Taking  the  mean  of  these  results,  we 
find  (1,255  +  1,591),  +  2  =  1423.  This  is  the  weight 
which,  according  to  the  rule,  the  piece  in  experiment 
5  should  have  borne,  and  it  varies  only  Gibs,  (less  than 
J  of  one  per  cent),  from  what  it  actually  did  bear. 

Again,  take  experiments  1  and  8  ;  in  which  the 
lengths  were  as  2  to  1.  Supposing  the  weights  to  be 
inversely  as  the  lengths,  and  as  the  squares  of  the 
lengths  successively,  and  taking  the  mean  of  the  re- 
sults,wehave  (1,980  +  8,960)  -^-2=2,970,  which  is  248ft>s. 
less  than  the  weight  borne  in  experiment  8.  But  it  is 
also  390Sbs.  greater  than  that  borne  in  experiment  7,  by 
a  piece  of  similar  form  and  dimensions,  but  an  inferior 
specimen.  It  does  not  seem,  therefore,  that  the  rule 
is  widely  at  fault. 

The  same  rule  applied  to  experiments  4  and  9, 
lengths  being  also  as  2  tol,  gives  2,784  Jfos.  as  the  bear 
ing  weight,  and  2,814  as  breaking  weight  for  No.  9  ;  the 
former  varying  71ibs.  and  the  latter  24ft>s.  from  the 
weights  shown  in  the  table.  IsTow,  if  we  observe  that 
the  one  broke  in  a  quarter  of  a  minute,  and  the  other 
endured  half  a  minute,  it  is  no  extravagance  to  assume 
that  if  No.  9  had  been  loaded  with  24Sbs.  less,  it  would 
have  stood  J  of  a  minute  longer,  giving  a  result  in  pre 
cise  accordance  with  the  rule. 

From  what  precedes,  it  is  believed  that  the  following 
may  be  adopted  as  a  safe  practical  rule  for  deter 
mining  the  power  of  resistance  to  compression,  for 
pieces  of  similar  cross-sections,  after  knowing  from 
experiment,  the  power  of  a  piece  of  given  dimensions, 
and  similar  cross  section. 


150  BRIDGE  BUILDING. 

Rule :  Make  'the  power  of  resistance  as  ~,  and  as  —  sue- 

L  li 

cessively,  and  take  the  mean  of  the  results  thus  obtained,  as 
the  true  result ;  D  representing  the  diameter  (or  width  of 
side,  in  square  pieces),  and  L,  the  length  of  the  piece. 
This  rule  will  be  probably  apply  without  material 
error,  to  pieces  of  lengths  from  15  to  40  times  as  great 
as  their  diameters,  and  perhaps  for  greater  lengths ; 
although,  in  bridge  building,  greater  lengths  will  sel 
dom  be  employed.*  But,  as  the  length  is  reduced  to 
8  or  10  diameters,  or  less,  it  is  manifest  that  the  power 
of  resistance  increases  at  a  less  rate  than  that  given  in 
the  rule.  For,  we  see  by  the  table  of  experiments, 
that  a  square  piece  of  a  length  equal  to  18  diameters 
(experiment  9),  bore  at  the  rate  of  45,0001bs.  to  the. 
square  inch,  which  is  nearly  one-half  of  the  average 
crushing  weight  of  cast  iron,  and  one-third  that  of  the 
strongest  iron.  But  according  to  the  rule,  a  piece  of 
half  that  length,  or  equal  to  9  diameters,  should  sustain 
135,000ibs.  which  is  about  the  maximum  for  cast  iron  ; 
whereas,  experiment  shows  that  the  power  of  resist 
ance  increases  with  reduction  of  length,  down  to  about 
2  diameters.  It  may,  therefore,  be  recommended  to 
apply  the  rule  above  given,  to  hollow  cylindrical,  and 
square  pieces  above  15,  and  to  solid  cylinders,  above 
12  diameters.  From  those  lengths  down  to  2  diame 
ters,  it  cannot  lead  to  material  error  to  estimate  an 
increase  of  power  proportionate  to  diminution  of 
length,  according  to  the  differences  between  the  weights, 
or  resisting  powers  determined  as  above,  for  square 
pieces  and  hollow  cylinders  of  15,  and  solid  cylinders  . 
of  12  diameters  in  length,  and  the  absolute  crushing 

*  It  is  probable  that' for  greater  lengths  than  40  diameters,  the  for 
mula  -j  alone,  would  be  more  nearly  sustained  than  in  case  of  smaller 
lengths. 


IRON  BRIDGES.  151 

weight  of  the  iron  ;  that  is,  if  a  square  piece  whose 
length  equals  15  diameters  bear  m  pounds,  and  the 
crushing  weight  for  pieces  of  2  diameters  be  n  pounds 
to  obtain  the  resistance  (R),  of  a  piece  of  (15 — a),  dia 
meters  in  length,  take  m  +  ~  (n — ?n)=R. 

XC.  It  has  already  been  remarked  that  in  practice, 
materials  should  be  exposed  to  much  less  strain  than 
their  absolute  strength  is  capable  of  sustaining  for  a 
short  time.  This  fact  is  universally  recognized,  and 
the  reasons  for  it,  are  perhaps,  sufficiently  obvious ; 
still  it  may  be  proper  to  mention  a  few  of  them  in  this 
place. 

First,  there  is  a  great  want  of  uniformity  in  the 
quality  and  strength  of  materials  of  the  same  kind, 
and  no  degree  of  precaution  can  always  guard  against 
the  employment  of  those  containing  defective  portions 
possessing  less  than  the  average  strength. 

Again,  when  materials  are  exposed  to  a  strain,  al 
though  it  be  but  a  small  part  of  What  they  can  ultimately 
bear,  a  change  is  produced  in  the  arrangement  of  their 
particles,  from  which  they  are  frequently  unable  fully 
to  recover  ;  and  whence  they  generally  become  weak 
ened,  especially  if  they  be  repeatedly  exposed  to  such 
process.  Hence,  it  often  happens  that  a  piece  is  broken 
with  a  smaller  strain,  than  it  has  previously  borne 
without  apparent  injury. 

Xow,  there  is  no  means  of  estimating  exactly  the 
allowance  necessary  to  be  made  on  account  either  of 
these  facts,  as  well  as,  probably,  many  others.  Con 
sequently,  we  can  not  determine  with  certainty,  how 
much  of  a  given  material  may  be  relied  on  to  sustain 
with  safety  a  given  force.  We  should  therefore,  incline 
toward  the  side  of  safety,  the  more  strongly,  in  pro- 


152  BRIDGE  BUILDING. 

portion  as  the  consequences  of  a  failure  would  be  the 
more  disastrous.  The  breaking  of  a  bridge  is  liable, 
in  most  cases,  to  be  a  serious  affair,  involving  hazard 
to  life  and  limb,  as  well  as  destruction  of  property. 
Hence,  they  should  be  constructed  of  such  strength 
asto  render  failure  quite  out  of  the  range  of  probability, 
if  not  absolutely  impossible. 

XCI.  Good  wrought  iron  bars,  will  not  undergo 
permanent  change  of  form  under  a  tensile  strain  of  less 
than  from  20,000  to  30,000  pounds  to  the  square  inch  ; 
and  though  they  will  not  actually  be  torn  asunder  with 
a  stress  below  50  or  60  thousand,  and  often  more,  to 
the  inch,  any  elongation  would  certainly  be  deleterious 
to  the  work  containing  them,  even  if  not  dangerous 
from  liability  to  fracture.  Hence,  it  is  certainly  not 
advisable  to  expose  the  material  to  a  stress  beyond  the 
lowest  limit  of  complete  elasticity. 

In  the  original  predecessor  of  this  work,  the  tra 
ditional  allowance  of  15,000ft>s.  to  the  square  inch,  was 
adopted  as  the  tensile  stress  to  which  wrought  iron 
might  safely  be  exposed,  and  beyond  which  it  was 
deemed  improper  to  rely  upon  it.  No  evidences  or 
arguments  since  that  time,  have  induced  a  change  of 
opinion  in  this  respect.  But  in  the  case  of  a  bridge, 
there  is  variety  and  uncertainty  as  to  the  exact  amount 
of  load,  as  well  as  in  relation  to  the  limit  of  safe  strain 
for  the  material ;  and  while  it  seemed  probable  that  the 
load  of  a  single  track  rail  road  bridge  would  never  ex 
ceed  2, OOOIbs.  to  the  lineal  foot  upon  any  part  of  its 
length,  still,  seeing  that  rail  roads  were  comparatively 
a  new  institution,  and  iron  bridges  for  rail  roads  almost 
unheard  of,  especially  in  this  country,  it  was  deemed 
wise,  in  recommending  their  introduction,  to  so  adjust 


Iiios  BRIDGES.  153 

their  proportions  as  to  meet  almost  any  possible  con 
tingencies. 

This  could  be  accomplished  either  by  assuming  a 
greater  possible  load  for  the  bridge,  or  a  lower  limit 
to  the  stress  of  materials  with  the  smaller  load,  with 
the  same  ultimate  result.  And,  perhaps  the  former 
would  have  been  the  more  consistent  course,  as  avoid 
ing  the  seeming  absurdity  of  the  assumption  that  iron 
could  safely  stand  a  strain  of  15,000ft)s.  in  a  common 
bridge,  but  only  10,000ft)  in  a  rail  road  bridge  ;  and  the 
no  less  seeming  absurdity  of  assuming  that  the  same 
material  could  stand  50  per  cent  more  strain  in  a  bridge 
composed  partly  of  wood,  than  in  one  entirely  con 
structed  of  iron.  Now,  instances  in  great  numbers 
could  be  pointed  out,  of  rail  road  bridges  of  wood  and 
iron,  where  2,0001bs.  to  the  lineal  foot  would  produce 
a  stress  considerably  exceeding  15,000  to  the  inch  upon 
certain  bolts  of  wrought  iron.* 

*  The  author  had  occasion  several  years  ago  to  refer  to  the  following 
instances  in  corroboration  of  the  statement  above  made,  in  this  wise 
"  The  best  evidence  that  exists  as  to  the  capacity  of  a  material  to  bear 
a  strain  with  safety,  is  derived  from  experience  as  to  the  strain  it  has 
been  exposed  to  in  works,  and  conditions  similar  to  those  in  which  it 
is  proposed  to  employ  it,  and  where  it  has  by  long  usage,  proved  itself 
adequate  to  the  labor  required  of  it.  If  wrought  iron,  for  example, 
has  been  used  in  railroad  bridges  for  a  great  number  of  years,  in 
numerous  and  repeated  instances,  where  a  given  load,  in  addition  to 
the  weight  of  structure,  would  produce  upon  it  a  tension  of  15,0001b  -i. 
to  the  square  inch,  and  has  withstood  such  usage  without  cases  of  fail 
ure  not  caused  by  manifest  defects  in  the  quality  of  material,  or  by 
casualties  which  such  structures  are  not  expected  to  be  proof  against  ; 
it  may  be  fairly  assumed  to  be  reasonably  safe  and  reliable  in  other 
railroad  bridges  where;  a  similar  gross  load  can  not  produce  a  greater 
stress  ;  and  much  more  so,  where  a  like  load  can  only  produce  a  stress 
one-half,  or  two-thirds  as  great. 

Now,  it  is  provided  in  the  plan  herewith  presented,  that  a  load  of 
2,00011)8.  to  the  lineal  toot  upon  each  pair  of  rails,  on  the  whole,  or 
any  part  of  the  length  of  the  bridge,  can  not  produce  upon  any  part  of 
the  wrought  iron  work  in  the  trusses,  a  tension  exceeding  10,0001bs. 
to  the  square  inch  ;  and,  to  show  that  such  provision  is  eminently  safe 
and  liberal,  I  proceed  to  give  some  examples  of  what  the  same  mate 
rial  is  liable  to  with  the  same  load  in  other  structures,  where  long  and 
severe  usage  has  fully  proved  its  sufficiency. 

16 


154 


BRIDGE  BUILDING. 


A  ud  yet,  it  was  deemed  expedient  by  the  author  of 
this  work,  in  the  outset  of  the  introduction  of  iron  rail 
road  bridges,  to  provide  that  2,000ft>s.  to  the  foot  upon 
each  pair  of  tracks,  should  not  give  a  stress  exceeding 
10,000ft)  to  the  square  inch  upon  any  part  of  the  wrought 
iron  work,  not  from  a  conviction  that  the  material  was 
unsafe  under  a  stress  of  15,000ft)s.  but  to  provide  against 
the  possible  contingency  of  its  being  sometimes  exposed 
to  greater  stress  than  that  produced  by  a  dead  weight 
of  2,000ib.  to  the  lineal  foot. 

XCII.  The  use  of  cast  iron  to  sustain  a  tensile 
strain,  should  undoubtedly  be  avoided,  as  a  general 


To  begin  with  an  instance  near  at  hand  ;  the  bridge  from  the  island 
to  the  main  shore  on  the  Hudson  River  rail  road  at  East  Albany,  has, 
in  one  of  its  stretches,  trusses  48  feet  long,  in  8  panels.  It  is  a  double 
track  bridge  with  three  trusses,  of  which  the  middle  one  sustains  one- 
half  of  the  two  pairs  of  tracks,  and  of  the  loaas  passing  over  them. 

The  truss  is  composed  of  top  and  bottom  chords,  and  thrust  braces 
of  timber,  and  vertical  suspension  bolts  of  wrought  iron,  in  pairs  ;  and 
it  is  at  once  obvious  that  £  of  the  weight  of  the  tracks  and  their  loads 
(or,  of  the  half  bearing  upon  the  centre  truss),  is  concentrated  on  the 
two  pairs  of  suspension  rods  located  6  feet  from  each  end.  [See  diagram.] 

The  weight  of  middle  truss,  and  other  parts  of  the  structure  sus 
tained  by  it,  probably  exceeds  16,000  Ibs.,  of  which  |,  or  14,000  Ibs.  bear 

FIG.  23 A. 


upon  the  endmost  suspension  bolts.  Add  2,000  Ibs.  per  foot  for  |  of  one 
pair  of  tracks,  or  rails,  and  it  makes  56,0001bs.  upon  the  suspension  bolts 
in  question,  with  only  one  track  loaded.  These  bolts  are  4  in  number, 
and  If"  in  diameter;  and,  allowing  -fa"  to  be  cut  away  by  screw 
thread,  the  aggregate  net,  available  cross  section  of  the  four,  is  equal 
to  4.43  square  inches  ;  whence  the  tension,  with  only  one  track  loaded, 
is  12,641  Ibs.  to  the  square  inch,  and  22,120  Ibs.  to  the  inch  with  both 
tracks  loaded. 

2.  The  bridge  leading  into  the  freight  house  of  the  Boston  rail  road, 
at  East  Albany,  is  a  "  Howe  bridge,"  and  acts  upon  the  same  princi 
ple  as  the  one  just  spoken  of.  It  is  a  double  track  bridge  with  two 
trusses,  having  8  panels  of  10' 8",  and  is  a  heavy  covered  bridge.  Al 
lowing  04  tons  for  weight  of  superstructure,  or  56,000  Ibs.  for  the  por 
tion  sustained  by  the  endmost  bolts  of  each  truss,  and  2,000  Ibs  per 
foot  upon  one  track,  of  which  $  at  least,  bears  on  one  truss,  giving 


IRON  BRIDGES.  155 

rule;  and,  if  on  certain  occasions  it  should  be  liable  to 
that  kind  of  action  to  a  small  extent,  the  stress  should 
probably  not  be  allowed  to  exceed  3,000  to  4, 000  pounds 
to  the  square  inch. 

When  exposed  to  compression,  in  pieces  of  such 
length  as  to  break  by  lateral  deflection,  it  is  believed 
it  may  be  safely  loaded  to  one-third  of  its  absolute  ca 
pacity.  If  a  long  piece  exposed  to  a  negative  strain 
have  a  defective  part,  it  does  not  diminish  its  power 
of  resistance  to  the  same  extent  as  when  it  acts  by  ten 
sion.  The  power  of  negative  resistance  being,  in  a 
measure,  inversely  as  the  deflection  produced  by  a 


100,000  Ibs.  on  the  end  bolts,  we  have  156,0001bs.  sustained  by  6  bolts 
of  iy  diameter,  containing  8.1  square  inches,  besides  screw  thread. 
This"  is  a  strain  of  19,259  Ibs.  to  the  square  inch  with  one  track,  and 
25,432  Ibs  with  both  tracks  loaded  with  2,000  Ibs.  to  the  lineal  foot. 

3.  The  East  bridge  over  the  creek  in  the  sonth  part  of  Troy,  is  a 
double  track   covered  bridge  with  three  trusses,  having  8  panels  of 
12'8"  each,  or  88.60  ft  sustained  by  the  endmost  suspension  bolts. 
Say,  of  weight  of  structure  bearing  on  end  bolts  of  middle  truss, 
86,000  Ibs.  and  of  load  upon  one  track  88,666,  making  123,666  Ibs.  on  4 
bolts  of  \¥'  diameter  and  two  of  If"  diameter,  having  a  net  cross-sec 
tion  of  about  7.65  square  inches.     Hence  the  stress  must  be  16,156  Ibs. 
to  the  inch,  with  one  track  loaded,  and  27,750  Ibs.,  with  2,000  Ibs.  to  the 
foot  upon  each  track. 

4.  The  West  bridge  over  the  same  stream,  a  few  rods  below  the  last 
mentioned,  has  three  trusses  containing  9  panels  of  10  £  ft.  each  in. 
length.     It  is  a  high  truss  bridge  with  roof  and  siding. 

For  weight  of  superstructure  on  endmost  bolts  of  middle  truss,  say 
28,000  Ibs.  and  for  load  on  one  track,  84,000,  making  112,000  Ibs.  on 
4  bolts  of  \\"  containing  a  net  section  ot  5.41  square  inches,  giving  a 
tension  of  20,702  Ibs.  to  the  inch  for  one  track,  and  36,229  Ibs.  for  both 
tracks  loaded  with  2,000  Ibs.  to  the  lineal  foot. 

5.  The  bridge  across  the  Erie  canal  near  Canastota,  on  the  N  Y.  C. 
B.  R.,  is  a  double  tack  bridge  with  2  trusses,  which  have  9  panels  of 
10  feet.     If  the  superstructure  be  estimated  to  weigh  40  tons,  it  gives 
a  little  over  35,000  Ibs.  on  the  end  bolts  of  each  truss.     Add  f  of  80 
tons  for  2,000  Ibs.  per  lineal  foot  upon  one  track,  and  it  gives  141,666  Ibs. 
on  4  bolts  of  \\"  diameter,  and  5.41  square  inches  of  net  cross-section  ; 
equal  to  26,173  Ibs.  to  the  inch,  with  one  track,  and  36,044  Ibs.  with  botk 
tracks  loaded." 

All  these  cases  are  stated  from  personal  examination  by  the  author, 
except  the  last,  which  was  reported  to  him  from  authority  considered 
reliable.  The  cases  were  not  selected,  but  taken  as  the  most  accessible, 
and  convenient  for  the  author's  observation.  And  still,  he  can  not 
help  regarding  them  as  remarkable,  and  somewhat  exceptional  cases 


156  BRIDGE  BUILDING. 

given  weight,  and  the  deflection  depending  on  the  stiff 
ness  of  the  piece  throughout  its  whole  length,  the 
power  is  manifestly  only  diminished  as  the  amount  of 
defect,  multiplied  by  the  ratio  of  length  of  the  defective 
part,  to  the  whole  length ;  that  is,  if  the  piece  be  de 
fective  so  as  to  lose  one-fourth  of  its  stiffness,  for  that 
part  of  its  length  to  which  is  due  one-tenth  part  of  the 
deflection,  the  deflection  will  only  be  increased  by 
Jx^  =  J0->  aud  the  power  of  resistance  is  diminished 
in  the  same  ratio ;  whereas  the  power  of  positive  re 
sistance  would  be  diminished  by  J. 

The  effect  of  negative  strain,  moreover,  is  believed 
not  to  be  so  deleterious  to  the  strength  of  iron,  as  that 
of  positive,  or  tension  strain ;  though  I  can  refer  to  no 
particular  facts  or  evidences  in  coroboration  of  the 
opinion. 

Upon  the  whole,  I  am  inclined  to  estimate  the  power 
of  cast  iron  to  resist  compression  (as  against  the  tension 
of  wrought  iron  at  15,0001bs.  to  the  inch),  in  pieces  of 
lengths  equal  to  18  diameters,  for  hollow  cylinders,  at 
15,000ft»s.  for  solid  cylinders,  at  8,000,  and  solid  square 
pieces,  at  10,000ibs.  to  the  square  inch  of  cross-section 

There  are  other  forms  of  section  for  cast  iron  mem 
bers  of  bridges,  which  it  will  frequently  be  convenient 
and  economical  to  employ  where  lateral  stiffness,  as 
well  as  longitudinal  resistance  is  required,  among  which 
may  be  named,  the  cruciform  +,  the  T,  and  the  H  form. 

The  former  of  these,  with  equal  leaves,  probably 
possesses  about  the  same  resistance  to  the  square  inch, 
.as  a  solid  square  which  will  just  contain  the  figure. 
For,  though  it  is  not  so  stiff  to  resist  a  simple  lateral 
force  diagonally  of  the  including  square,  as  parallel  with 
its  sides,  and  would  be  broken  by  tearing  asunder  the 
flange,  or  leaf  upon  the  convex  side,  still  when  under 


NEGATIVE  STRENGTH  OF  IRON.  157 

longitudinal  compression,  the  tension  upon  that  leaf 
would  be  so.mewhat  relieved. 

The  T  and  H  section  will  usually  be  employed  where 
greater  stiffness  is  required  in  particular  directions,  and 
if  proportioned  with  judgment,  will  usually  possess  about 
the  same  power  to  the  inch,  as  the  including  a  olid  square, 
or  parallelepiped. 

XCIII.  Having  determined  (approximately,  at  least)^ 
the  safe  strain  for  pieces  of  a  certain  length,  and  the 
ratio  of  variation  in  power,  depending  upon  change  of 
length,  we  readily  deduce  the  safe  strain  for  pieces 
of  similar  action,  with  any  given  dimensions. 

The  following  table,  exhibiting  the  negative  power 
of  resistance  to  the  square  inch  of  cross-section,  for 
hollow  and  solid  cast  iron  cylinders,  and  solid  square 
pieces  (under  which  class  may  be  included  the  -f  T  and 
H  formed  sections,  under  proper  conditions),  calculated 
for  length  of  from  2  to  60  diameters,  is  intended  to 
show  the  safe  practical  rate  of  strain  for  the  material, 
being  about  one-third  of  its  absolute  strength,  in  col 
umns  headed  J,  and  one-fourth  of  the  absolute,  in  those 
headed  J ;  the  former  to  be  used  against  wrought  iron 
at  15,000,  and  the  latter,  where  wrought  iron  is  esti 
mated  to  sustain  10,OOOIbs.  to  the  square  inch. 

This  is  the  author's  original  table,  slightly  modified  5 
with  the  addition  of  two  columns  showing  corresponding 
weights  at  J  and  J  of  the  absolute  strength,  as  calculated 
by  "Gordon's  formula,"  deduced  from  Hodgkinson's, 
experiments  upon  cast  iron  hollow  pillars;  which  is 
regarded  as  the  best  authority  upon  the  subject  at  the 
present  day.  Also,  two  corresponding  columns  for 
wrought  iron  hollow  pillars,  according  to  the  same  au 
thority. 


158  BRIDGE  BUILDIXQ. 

The  Gordon  formulae  are  : 

for  cast  iron,  S  =  80,000ft).  -r-  (1+  .0025^), 

for  wrought  iron,  S  =  36,000ibs.  -4-  (1  -f  .00033|). 

S  representing  absolute  strength  per  square  inch 
of  section,  £,  the  length,  and  d,  the  diameter  of  column, 
both  referring  to  the  same  unit  of  length.  Or  making 
d  =  1,  we  have  —  =  I2. 

The  table  of  negative  resistances,  presents  a  scale  of 
numbers  so  adjusted  as  to  touch  at  certain  points  esta 
blished  by  experiment,  and  running  in  consistent  gra 
dations  from  one  to  another  of  such  points. 

The  columns  for  cast  iron  hollow  cylinders,  are  the 
only  ones  referring  to  the  same  class  of  pieces,  and  ex. 
hibiting  the  difference  in  results,  arising  from  differ 
ence  in  the  mode  of  calculation.  The  Gordon  formula 
is  supposed  to  give  results  agreeing  with  those  of  ex 
periment,  for  lengths  included  within  the  range  em 
braced  by  the  experiments  from  which  the  formula 
was  deduced.  "Within  that  range,  those  results  may 
be  presumed  to  be  more  reliable  (being  founded  on 
trials  of  the  same  kind  of  pieces  as  those  to  which  they 
refer),  than  those  in  the  author's  original  table,  based 
upon  trials  of  solid  cylinders  and  parallelepipeds. 

Taking  the  4th  and  6th  columns,  it  will  be  seen  that 
the  numbers  agree  at  some  point  between  the  lengths 
of  18  and  20  diameters;  the  numbers  above  that  point, 
being  the  larger  in  column  6,  while,  below  that  point, 
they  are  larger  in  column  4,  down  to  about  50  diame 
ters,  where  they  come  together  and  cross  again,  and 
those  in  6,  are  thenceforward  the  larger.  But  the 
differences  are  small,  for  the  range  of  lengths  princi 
pally  employed  in  bridge  work. 


•2* 


L 

d 


NEGATIVE  STRENGTH  OF  IRON. 


159 


+1 


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160  BRIDGE  BUILDING. 

One  obvious  reason  of  the  more  rapid  increase  of 
numbers  in  the  6th  column,  for  lengths  under  15  or 
16  diameters,  is,  that  in  the  latter,  the  crushing  weight 
for  the  iron  is  assumed  at  100,OOOIbs.  to  the  square 
inch,  whereas,  by  the  Gordon  formula  it  is  limited  at 
80,OOOIbs,  and  that  formula  can  give  no  result  greater 
than  that  limit,  even  when  Z=0.  Now,  if  80,0001bs. 
was  less  than  the  actual  crushing  load  for  the  kind  of 
iron  used  in  Hodgkinson's  experiments  (from  which 
the  Gordon  formula  is  understood  to  have  been  de 
rived),  it  must  follow  that  Gordon's  formula  gives 
results  smaller  than  the  true  ones,  for  short  pieces. 
This  is  probably  the  case,  and,  although  Mr.  Gordon's 
formula  is  very  simple  and  ingenious,  sliding  smoothly 
and  plausibly  from  one  extreme  in  length  to  the  other, 
it  unquestionably  gives  closer  approximations  to 
correct  results  for  the  ordinary  range  of  lengths,  than 
when  applied  to  the  very  short  pieces. 

The  numbers  in  the  table  are  deduced  upon  the  sup 
position  that  the  thrust  members  in  a  bridge,  will  not 
act  with  less  advantage  than  when  bearing  upon  a  pivot 
at  each  end  of  the  axis  of  the  pieces  respectively  ;  and 
it  is  not  deemed  proper  to  assume  that,  in  consequence 
of  having  flat  end  bearings,  the  piece  in  any  case  can 
sustain  a  greater  stress  than  is  indicated  by  the  num 
bers  in  the  table. 

It  will  be  observed  that,  in  order  to  obtain  the  ab 
solute  strength  of  a  piece,  we  should  multiply  its  cor 
responding  number  in  the  table,  by  the  denominator 
of  the  fraction  (J  or  J)  at  the  head  of  the  column. 


LATERAL,  OR  TRANSVERSE  STRENGTH.         161 


.  26. 


LATERAL,  OR  TRANSVERSE  STRENGTH. 

XCIV.  The  transverse  strength  of  bars  or.  beams, 
would  seem  to  be  deducible  from  the  positive  strength 
of  the  material,  in  the  following  manner : 

Let  ab,  Fig.  26,  represent  a  portion  of  a  rectangular 
beam  or  bar,  projecting  from  a  wall  in  which  it  is 

firmly  fixed.  If  a  weight  be 
applied  at  w,  the  upper  part 
of  the  beam  will  be  extended, 
and  the  lower,  compressed  ; 
and,  where  these  portions 
meet,  is  what  is  called  the 
neutral  plane.  Experiment 
shows  that  this  plane,  in 
rectangular  beams,  is  central  between  the  upper  and 
lower  surfaces ;  or  at  least,  very  nearly  so,  for  all 
elastic  substances,  until  they  approach  rupture. 

The  tendency  of  the  weight  at  w,  then,  is  to  produce 
rotation  about  the  point  c  (or,  the  line  of  intersection 
of  neutral  plane  and  face  of  wall)  and  the  cohesion  of 
the  upper  portion  cd,  and  the  repulsion  of  the  lower 
part,  cb,  tend  to  resist  rotation.  Now,  to  determine 
the  amount  of  this  resistance,  which  is  the  measure  of 
transverse  strength,  we  will  first  consider  the  upper 
portion ;  and  it  is  obvious  that,  at  every  part  of  the 
cross-section,  the  resistance  to  rotation  is  as  the 
resistance  to  extension,  multipled  by  the  distance  of 
the  part  above  the-  neutral  plane.  But  the  resistance 
to  extension,  by  the  law  of  elasticity,  is  as  the  degree, 
or  amount  of  extension,  which  is  determined  by  the 
distance  from  the  neutral  plane  ;  parts  at  2  inches  from 
this  plane,  or  the  centre  of  motion,  being  extended 
21 


162  BRIDGE  BUILDING. 

twice  as  much  as  those  at  one  inch,  and  resisting  twice 
as  much. 

Then,  denoting  the  distance  from  this  plane  by  the 
variable,  quantity  x,  the  resistance  to  extension  by  any 
part,  equals  x  multiplied  by  a  certain  constant  (s),  and 
may  be  denoted  by  sx,  while  the  resistance  to  rotation 
about  c,  equals  sx2. 

Again,  representing  the  horizontal  breadth  or  thick 
ness  of  the  beam  by  /,  we  have  t.dx  to  represent  the 
differential  of  the  section  (in  its  state  of  increase  from 
c  toward  d),  and  s.t.x2dx,  the  differential  of  resistance. 
Then,  integrating,  aud  making  x  =  cd  —  A,  we  have  the 
whole  resistance  to  rotation,  of  the  part  above  the  neu 
tral  plane,  equal  to  J  s.t.h3  =  ^t.hxhxs.h.  But  s.h 
becomes  equal  to  the  positive  strength  of  the  material 
when  x=cd  =  A,  and  t.h  =  the  area  of  section  above 
the  neutral  plane.  Therefore  the  power  of  this  part  to 
resist  rotation,  is  equal  to  J  of  the  area,  multiplied  by 
half  the  depth  of  the  beam,  and  by  the  positive  strength 
of  the  material;  in  case  the  negative  strength  exceed 
the  positive. 

Now,  it  is  obvious  that  the  part  below  the  neutral 
plane  exerts  exactly  the  same  amount  of  resistance  to 
rotation,  as  the  part  above.  Therefore  the  whole  power 
of  resistance  to  rotation  about  c,  in  other  words,  the 
resistance  to  rupture,  is  equal  to  J  of  the  whole  cross- 
section,  multiplied  by  J  the  depth  of  beam,  and  by  the 
positive,  or  cohesive  strength  of  the  material ;  that  is 
equal  to  J  C.t.Dx^D,  =  £  C,t.D2 ;  in  which  expression, 
D  represents  the  depth  ((/6),  and  (7,  frhe  cohesive  power 
of  the  material.* 

*  Another  mode  of  illustrating  this  case,  is  the  following1 :  It  being1  ob 
vious  that  the  resistance  to  rotation  about  c,  by  each  lamina  from  the  neu 
tral  plane  outward,  is  as  the  extension  it  undergoes,  and  the  leverage 
upon  which  it  acts,  such  resistance  must  increase  outward  in  u  duplicate 


LATERAL,  OR  TRANSVERSE  STRENGTH.         163 

If  we  wish  to  determine  the  greatest  weight  (W), 
which  the  beam  is  capable  of  bearing  when  applied  at 
any  horizontal  distance  (L)  from  c  or  d,  we  institute 
the  equation,  W.L  =  J  C.t.D2  ;  whence  we  have  : 


6L  % 

This  formula  applies  to  all  projecting  rectangular 
beams,  when  the  force  (W),  acts  parallel  with  the 
sides,  and  L  represents  the  nearest,  or  perpendicular 
distance  of  the  fulcrum  <?,  from  the  line  in  which  the 
force  has  its  action  :  provided,  that  if  the  material 
have  greater  power  to  resist  tension  than  compression, 
C  is  to  be  taken  as  representing  the  repulsive,  instead 
of  the  cohesive  power. 

XCY.  This  formula  is  deduced  on  the  supposition 
that  the  material  is  perfectly  elastic,  so  as  to  suffer  no 
permanent  change  of  form  until  the  strain  produces 
actual  rupture.  There  are  few  substances  if  any,  and 
certainly  wood  and  iron  are  not  such,  that  fulfill  this 
condition  so  nearly  but  that  considerable  discrepan 
cies  are  found  between  the  deductions  of  theory,  and 
the  results  of  experiment.  Indeed  in  the  case  of  cast 


ratio  to  the  increase  of  distance  from  that  plane,  and  decrease  in  a  like 
ratio,  inward.  Hence,  if  we  represent  the  resistance  of  the  outer  lamia 
by  the  base  of  a  pyramid  having  its  apex  at  the  neutral  plane,  and  its 
base  coinciding  with  said  outer  lamina,  the  resistance  of  any  other 
lamina  will  be  represented  by  the  section  of  the  pryamid  made  by 
snch  lamina,  or  a  lamina  of  the  pryamid  at  the  point  of  intersection, 
of  the  same  (indefinitely  small)  thickness  as  the  lamina  of  the  beam 
in  question  ;  and  the  sum  of  resistances  of  all  the  laminae  of  the  beam, 
will  be  represented  by  the  Bum  of  laminae  of  the  pyramid  ;  and  will 
bear  the  same  ratio  to  what  the  resistance  of  all  those  lamina?  of  the 
beam  would  be,  if  all  were  acting  at  the  distance  of  the  outermost 
lamina,  as  the  solidity  of  the  pyramid  bears  to  a  prism  of  like  base 
aud  attitude  ;  that  is,  in  the  ratio  of  1  to  3.  But  the  resistance  of  the 
outer  lamina,  equals  the  absolute  strength  of  material  (C),  multiplied  by 
half  the  depth  of  beam.  Hence,  the  resistance  of  tlie  half  beam  equals 
Cxi  cross-section  X  depth  of  the  half  beam  ;  being  the  same  result 
as  above  obtained  by  integration.  , 


164  BRIDGE  BUILDING. 

iron,  experiment  shows  the  transverse  strength  to  be 
fully  twice  as  great  as  it  is  made  to  appear  by  the  above 
formula. 

If  in  the  expression  —5!,  we  make  L=D,  it  may  be 
reduced  to  £  C.t.D\  showing  that  the  power  of  a  pro 
jecting  'rectangular  beam  to  sustain  weight  at  a  dis 
tance  from  the  fulcrum  equal  to  the  depth  of  the  beam, 
is  only  one-sixth  as  great  as  the  positive  (or  negative, 
in  case  that  be  the  smaller),  strength  of  the  material. 
This  is  a  convenient  way  of  expressing  transverse 
strength,  viz :  as  equal  to  a  force  of  so  many  pounds 
to  the  square  inch  of  cross-section,  the  force  being  un 
derstood  as  acting  upon  a  leverage  equal  to  the  breadth 
of  the  beam  in  the  direction  of  the  acting  force. 

If  we  call  18,000ft>s.  to  the  square  inch,  the  positive 
strength  of  cast  iron,  we  may  call  the  transverse 
strength  (according  to  the  above  deduction),  \  18,000 
=3,0001bs. ;  meaning  that  a  bar  one  inch  square  will 
sustain  upon  its  projecting  end,  3,OOOIbs.  at  1  inch 
from  the  fulcrum,  and  proportionally  less,  as  the  dis 
tance  is  greater. 

^"ow,  experiment  shows  that  it  will  sustain  twice  this 
amount,  and  frequently  more,  so  that  we  may  in  reality, 
reckon  the  transverse  strength  of  cast  iron  at  about 
6,000ft>s.  to  the  square  inch. 

I  know  of  nothing  to  which  to  attribute  this  great 
discrepancy  between  theory  and  experiment,  except  a 
want  of  complete  elasticity  in  the  material,  and  per 
haps,  also  to  the  assumption  of  too  low  an  estimate 
(18,000)  Bbs.  for  the  co-hesive  power  of  cast  iron. 

Cast  iron,  when  exposed  to  a  transverse  strain,  suf 
fers  extension  on  one  side,  and  compression  on  the 
other ;  and  the  power  of  resistance  to  both  these  effects, 
increases  very  nearly  as  the  amount  of  extension  or 


LATERAL,  OR  TRANSVERSE  STRENGTH.         165 

compression,  until  a  certain  point  or  maximum  is 
reached,  and  after  passing  this  point,  the  power  dim 
inishes.  Now,  it  is  reasonable  to  suppose,  in  fact  we 
can  hardly  suppose  the  contrary,  that  for  a  certain  in 
terval  on  each  side  of  the  maximum  point,  the  power 
of  resistance  remains  nearly  stationary.  But  this  sta 
tionary  interval  is  reached  on  the  positive,  much  sooner 
than  on  the  negative  side,  and  the  inevitable  conse 
quence  must  be,  that  the  neutral  plane  is  transferred 
further  from  the  positive  side,  so  as  to  preserve  the 
equilibrium  between  the  resistance  to  extension  and 
the  resistance  to  compression.  Hence,  the  amount  of 
resistance  on  the  positive  side  is  increased,  both  by  the 
increased  area  of  section  exposed  to  tension,  and  in 
creased  leverage,  or  distance  from  the  neutral  plane. 

Moreover,  a  greater  portion  of  the  fibres  (so  to  speak), 
of  extension,  act  with  their  full  power;  since,  while 
the  outside  portion  is  passing  through  what  we  have 
called  the  stationary  interval,  successive  portions  toward 
the  neutral  plane,  are  reaching  and  approaching  that 
interval.  Hence,  some  considerable  proportion  of  all 
the  fibres  of  extension,  may  act  with  their  maximum 
power ;  whereas,  if  the  material  were  perfectly  elastic 
up  to  the  point  of  actual  rupture,  only  the  outside  fibres 
farthest  from  the  neutral  plane,  could  act  with  abso 
lute  power,  and  all  other  parts,  only  in  the  ratio  of 
their  respective  distances  from  said  plane.  To  illus 
trate,  suppose  the  extreme  positive  side,  when  ex 
tended  one  inch,  reach  the  stationary  interval,  which 
is  one  inch  more.  It  follows  that  when  the  outside 
has  passed  to  the  other  limit  of  that  interval,  one-half 
of  the  positive  portion  of  the  bar,  will  be  within  the 
the  range  of  that  interval,  and  act  with  its  maximum 
power,  producing  one  third  more  resistance  to  exten- 


166  BRIDGE  BUILDING. 

sion  than  the  same  fibres  could  afford  if  the  body  were 
perfectly  elastic,  up  to  the  point  of  rupture.  I  know 
of  no  more  plausible  manner  of  explaining  the  observed 
discrepancy  between  experiment  and  calculation  upon 
the  subject. 

But,  having  well  authenticated  direct  experimental 
evidence  as  to  the  transverse  strength  of  cast  iron,  we 
may  safely  be  guided  thereby;  and,  though  it  would 
be  a  satisfaction  to  find  a  complete  agreement  between 
the  results  of  direct  experiments,  and  the  deductions 
from  those  that  are  indirect,  still,  where  such  agree 
ment  is  not  found,  the  direct  evidence  should  have  the 
preference.  We  may,  therefore,  regard  the  transverse 
strength  of  cast  iron  in  pieces  with  rectangular  sec 
tions,  as  equal  to  6,OOOIbs.  to  the  square  inch,  upon  a 
leverage  equal  to  the  width  of  the  piece  in  the  direction 
of  the  force. 

"Wrought  iron  has  something  over  three  times  the 
positive  strength- of  cast  iron,  on  the  average;  and  if 
we  consider  its  transverse  strength  to  be  in  the  same 
ratio  to  that  of  cast  iron,  its  transverse  strength  would 
be  about  20,000  pounds.  That  is,  the  projecting  end 
of  a  bar  of  wrought  iron  one  inch  square,  should  sus 
tain,  at  one  inch  from  the  fulcrum,  a  weight  of  20,000ft>s 
But  it  becomes  permanently  bent  with  about  one-third 
of  that  weight,  and  therefore,  in  practice  it  should  not 
be  exposed  to  more  than  4,000  to  5,OOOSbs.  as  we  should 
manifestly  keep  within  the  elastic  limit,  as  well  in  case 
of  a  transverse,  as  a  direct  tensile  strain.  It  may, 
therefore,  be  recommended  to  estimate  the  transverse 
strength  of  wrought  iron  at  5,000fts.  as  against  a  ten 
sile  strain  of  15,OOOJbs.  to  the  inch,  upon  the  same  ma 
terial,  and  3,500  to  4,000  transverse,  against  10,000, 
tensile  strain. 


LATERAL,  OR  TRANSVERSE  STRENGTH.         167 

Cast  iron  having  an  average  absolute  transverse 
strength  of  6,000ft)3.  should  not  in  practice,  be  exposed 
to  over  from  1,000  to  l,5001bs.  to  the  square  inch,  ac 
cording  to  the  circumstances  in  which  it  is  used. 

XCVI.  Representing  by  A  the  area  by  D  the  depth 
and  by  L  the  length  (from  fulcrum  to  weight)  of  a  pro 
jecting  rectangular  beam,  the  safe  load,  according  to 

the  above  assumptions,  equals  5,000  —  for  wrought, 

and  1,500  —for  cast  iron. 

If  the  beam  be  supported  at  the  ends  and  loaded  in 
the  middle,  using  the  same  symbols,  the  safe  load  is 
four  times  as  much  ;  that  is,  20,000  —  for  wrought, 

LJ 

and  6,000  —  for  cast  iron.  This  follows  from  the  fact 
that  the  lifting  force  at  each  end,  equals  only  one-half 
of  the  load,  and  acts  upon  a  leverage  equal  to  -JL,  hence 
it  takes  4  times  the  weight  to  produce  the  same  stress 
on  the  beam. 

If  the  load  be  equally  distributed  over  the  length  of 
the  beam,  the  safe  load  is  twice  as  much  as  when  it  is 
concentrated  at  the  end  of  the  projecting  beam,  and  in 
the  middle  of  the  beam  supported  at  the  ends.  For, 
in  the  former  case,  each  part  of  the  weight  produces 
stress  at  the  fulcrum  in  proportion  to  its  distance  there 
from,  and  the  average  distance  of  the  whole  load, 
being  only  half  as  great,  the  stress  is  only  half  as  much 
as  when  the  whole  load  is  at  the  end. 

In  the  latter  case,  the  beam  being  regarded  as  fixed 
in  the  centre,  the  lifting  force  at  the  end,  tends  to  pro 
duce  a  strain  in  the  centre,  measured  by  the  force  mul 
tiplied  by  its  distance  from  the  centre,  in  other  words, 
by  the  moment  of  the  force  with  respect  to  the  centre. 
On  the  contrary,  the  load  tends  to  produce  a  strain  in 


168  BRIDGE  BUILDING. 

the  opposite  direction,  according  to  the  distance  of 
each  part  of  the  load  from  the  centre.  This,  as  just 
seen  in  the  case  o£  the  projecting  beam,  is  equal  to 
half  of  that  produced  by  the  lifting  force  at  the  end. 
Hence  the  effect  of  the  weight  neutralizes  one-half 
of  tendency  of  the  lifting  force  at  the  end,  to  produce 
stress  in  the  centre  of  the  beam. 

Upon  the  same  principle  is  based  the  following  rule 
for  determining  the  stress  at  any  given-point  in  the  length 
of  a  beam,  however  the  load  may  be  distributed. 
Take  the  moment  with  respect  to  the  given  point,  of 
all  the  forces  on  either  side  of  said  point,  tending  to 
deflect  the  beam  in  one  direction,  at  the  given  point, 
and  all  the  forces  on  the  same  side,  tending  to  deflect 
it  in  the  opposite  direction,  and  the  difference  in  the 
sums  of  those  opposite  moments,  is  the  measure  of  the 
stress  at  the  point  in  question. 

As  an  illustration,  if  the  cross-beam  of  a  rail  road 
bridge  support  tracks  5'  apart,  the  beam  being  15'  be 
tween  supports,  and  a  weight  W  bear  equally  upon 
the  two  tracks,  each  end  support  lifts  JW,  and  the 
moment  with  respect  to  the  nearest  track,  is  JWx5  = 
2.5W.  There  being  no  force  acting  in  the  opposite 
direction  between  the  end  and  the  weight  upon  the 
rail,  2.5W  (upon  a  leverage  of  1  foot),  is  the  measure 
of  stress  of  the  beam  at  the  rail. 

If  we  seek  the  stress  in  the  middle  of  the  beam  7J' 
from  the  end,  and  2J'  from  the  rail,  the  upward  force 
at  the  end  is  JW,  the  same  as  before,  and  the  moment 
jWx7J  =  3.75W;  while  the  moment  of  the  weight 
on  the  rail,  is  |Wx2J,  =  1.25W.  Hence,  the  stress 
in  the  centre  =  (3.75 — 1.25)W  =  2.5W,  the  same  as  at 
the  rail. 


LATERAL,  OR  TRANSVERSE  STRENGTH.         169 

Taking  the  moment  of  the  end  lift  with  respect  to 
the  off  rail,  we  have  jWxlO,  =  5W,  while  the  moment 
of  weight  on  the  near  track,  with  respect  to  the  off 
track,  is  J  Wx5,  =  2JW,  acting  in  the  opposite  direc 
tion.  Hence,  stress  at  the  off  track,  is  equal  to  (5 — 2. 5) W 
=  2JW. 

Again,  assuming  a  point  at  2'  from  the  end,  the  mo 
ment  of  the  lift  at  the  farther  end,  is  J  W  X  13'  =6.5W. 
The  sum  of  moments  of  weights  upon  the  two  jails  is, 
J\Vx8-fJWx3  =5.5W  in  opposition  to  the  effects 
of  the  end  lift.  The  stress  of  the  heam,  therefore,  at 
the  given  point,  is  (6.5  — 5.5) W,  =  W  ;  being  the  same 
result  as  if  we  had  taken  the  moment  at  the  near  end, 
=  JW'X  2,  =  W,  with  no  opposite  force  on  the  same 
side  of  the  given  point. 

Hence,  we  see  that  the  stress  is  the  same  at  all  points 
between  the  rails,  while  it  obviously  diminishes  from 
the  rail  to  the  end,  in  proportion  as  the  distance  of 
successive  points  from  the  end  diminishes.  Therefore, 
the  beam  having  a  uniform  depth,  in  order  that  the 
strain  be  uniform  on  all  parts,  the  thickness  should 
taper  uniformly  from  the  rail,  to  an  edge  at  the  sup 
porting  points.  If  the  thickness  be  uniform  (the  cross- 
section  being  rectangular),  the  depth  may  diminish  as 
the  square  root  of  distance  from  the  support  diminishes; 
that  is,  may  have  a  parabolic  form,  This  follows  from 
the  fact  that  the  stress  at  different  points  in  the  length 
is  as  the  distance  from  the  support,  and  the  power  of 
resistance,  as  the  area  multiplied  by  the  depth,  in  other 
words,  as  the  square  of  the  depth,  the  area  being  simply 
as  the  depth. 

XCVII.  Iron  beams  of  a  rectangular  section  will 
seldom  be  used  in  bridge  work,  the  material  acting 
22 


170  BRIDGE  BUILDING. 

n\ore  effectually  in  a  web  and  flange  form,  as  in  the  I 
beam,  with  about  half  the  material  in  the  flanges.  In 
this  kind  of  beam,  the  web  may  be  estimated  as  a  rect 
angular  beam  —  say  at  5,OOOIbs  to  the  inch  (on  a  lever 
age  equal  to  the  depth  of  the  beam),  while  the  flanges 
may  be  estimated  at  15,000ft>s  upon  a  leverage  of  half 
the  depth  of  beam,  less  half  the  thickness  of  flange, 
thus :  for  a  beam  12"  deep,  web  \"  thick,  flanges  2" 
wide  and  f"  in  average  thickness  on  each  side  of  the 
web,  we  have  6  square  inches  of  web  section  at  5,000  = 
30,0001bs.  plus,  6  inches  of  flange  section  at  15,000  X 
leverage  of  5,625",  equal  to  42,187ft>s.  on  a  leverage  of 
the  depth  of  beam,  making  a  total  of  72,187ft>.  ==6,015ft>s. 
to  the  inch  upon  the  whole  section. 

Hence,  it  is  deemed  safe  to  estimate  the  working 
strength  per  square  inch  of  wrought  iron  I  beams,  in 
the  above  proportions  of  web  and  flanges,  at  6,000 
— Ibs.  for  projecting  ends,  and  24,000 -for  beams  sup 
ported  at  the  ends,  and  loaded  in  the  middle ;  and 
double  those  amounts  of  distributed  load.  For  instance  ; 
a  12"  I  beam  of  12  square  inches  in  section,  and  16' 
long,  between  bearings,  is  good  for  24,000  X  ]§  =F 
18,000ft)s.  in  the  middle,  36,000  distributed  uniformly, 
and  26,1801bs.  upon  two  rails  5  feet  apart,  or  5.5  feet 
from  end  supports. 

XCVIII.  One  of  the  cases  in  which  wrought  iron 
is  frequently  exposed  to  transverse  strain,  is  in  the  use 
of  cylindrical  pins  for  connecting  the  other  parts  of 
bridge  work.  In  such  cases,  the  forces  will  act  with  a 
certain  leverage  which  can  be  nearly  determined.  The 
power  of  a  round  pin  to  sustain  a  transverse  force  act 
ing  on  a  leverage  equal  to  the  diameter,  may  be  as 
sumed  at  about  T^  less  to  the  square  inch,  than  that  of 


LATERAL,  OR  TRANSVERSE  STRENGTH.         171 

a  square  bar  upon  a  leverage  equal  to  its  width  of  side. 
Hence,  A  representing  the  area  of  section,  D,  the  diame 
ter,  and  L,  the  length,  the  safe  stress  =  4,500  A~  acting 

on  a  projecting  end,  and  18,000-—  acting  in  the  middle 
between  two  outside  bearings ;  that  is,  a  V  pin  with 
centres  of  outside  bearings  6"  apart,  will  bear  in  the 

middle,  18,000  X '—  =  2,355ft>s.     If  the  pin  connect  an 

eye  V  thick,  between  one  of  \"  thick  on  each  side,  the 
length  (L)  between  centres  of  outside  pieces,  will  be 
1£";  whence,  a  V  pin  will  bear  4  times  as  much  as  in 
the  preceding  case;  or  2,355  x  4  =  9,420ft)3.  The 
tensile  strength  of  a  1"  round  rod,  being  ll,7751bs. 
being  equal  to  the  cross-section  (0.785),  X  15,OOOR)s.  it 
$hows  that  the  strength  of  the  rod  is  greater  than  that 
of  the  pin,  in  the  condition  here  assumed,  in  the  pro 
portion  of  11,775  to  9,420.  Therefore,  the  stiffness  of 
the  pin  being  as  the  cube  of  the  diameter,  in  order  to 
find  the  diameter  (#),  of  a  pin  for  connecting  V  bars 
by  eyes  and  connecting  straps,  we  have  this  proportion 
9,420  :  11,775  :  :  I3  :x3,  whence  z  =  1.077  =  to  about 
-1*3  larger  than  the  diameter  of  the  rods  to  be  connected, 
and  in  this  proportion  for  any  size  of  round  rods  con 
nected  by  straps  and  pins  or  bolts. 

But  if  the  eyes  and  straps  be  drilled,  so  as  to  fit  the 
pin  through  the  whole  thickness,  the  action  approaches 
the  shear  strain,  and  the  pin  should  have  about  f  the 
area  of  section  of  the  bars  to  be  connected.  The  author 
would  recommend,  however,  for  general  practice,  that 
connecting  pins  be  considered  as  acting  by  transverse 
stiffness,  upon  the  lever  principle,  as  above  discussed. 


172 


BRIDGE  BUILDING. 


ARCH  TRUSS  BRIDGES.  173 


ARCH  TRUSS  BRIDGES. 

XCIX.  The  general  form  in  outline  of  the  Arch 
Truss,  may  be  seen  in  Figs.  8  and  11. 

The  forms  of  the  different  members,  and  the  modes 
of  connecting  them  to  form  the  complete  structure,  are 
many,  and  a  minute  description  of  each  possible  variety, 
in  this  respect,  even  if  such  a  thing  can  be  regarded  as 
practicable,  will  not  be  undertaken  on  this  occasion. 

The  arch  may  be  of  cast  or  wrought  iron  in  various 
forms  of  section.  The  following  form  of  cast  iron  arch 
has  been  extensively  used  in  the  state  of  New  York, 
with  uniform  success  and  satisfaction.  The  arch  is 
composed  of  cast  iron  sections,  equal  in  number  to 
the  number  of  panels  in  the  truss ;  an  odd  number 
being  deemed  preferable.  In  Fig.  27,  o.  on  m  presents 
a  top  view  of  the  arch,  and  D,  a  top  view  of  the  chord, 
from  end  to  centre;  'and  A  and  B,  enlarged  cross-sec 
tions  at  p  and  </,  adjacent  to  the  cross-bars  to  be  de 
scribed  below,  and  which  also  appear  in  the  figure. 
Each  piece  consists  of  two  side  portions  of  an  ~~|  formed 
section,  connected  at  the  ends,  and  at  2  or  3  intermedi 
ate  points,  by  cross-bars  of  a  J  formed  section  for  the 
intermediates,  and  at  the  ends,  with  sections  as  seen  at 
(7,  where  a  view  of  the  arch  connection  is  shown,  as  it 
would  appear  if  cut  vertically  and  longitudinally 
through  the  centre,  and  the  near  half  removed. 

The  width  of  the  side  plates  of  arch  castings  (from 
the  top),  should  be  about  ^  of  the  length  of  pieces, 
with  an  average  thickness  of  from  T^  to  J  of  the  width. 
The  top  plate,  about  the  same  thickness  (or  a  trifle  less, 
to  prevent  a  tendency  in  the  piece  to  become  hollow 


174  BRIDGE  BUILDING. 

backed  in  cooling),  and  a  width,  a  little  over  one-half 
that  of  the  side  plate. 

The  resisting  power  may  be  estimated  as  in  the  table 
of  negative  resistances  under  the  head  of  square,  &c., 
pieces,  calling  the  width  of  side  plates  the  diameter, 
and  using  the  column  under  J,  for  trusses  supporting 
12  feet  or  more  width  of  flooring,  and  the  column 
headed  J,  in  case  of  trasses  supporting  a  width  of  10 
feet  or  less,  to  each  truss. 

The  intermediate  cross  bars  should  have  about  the 
same  thickness  of  plate  as  the  side  portions,  a  depth, 
about  f  that  of  side  plates,  and  top  plate  not  less  than 
f  as  wide  as  the  top  plate  of  side  portions. 

End  cross-bars  should  have  a  top  width  of  about  f 
the  width  of  side  plates,  and  cross-section  sufficient  to 
sustain  a  whole  gross  panel  load  for  the  truss,  by  trans 
verse  resistance.  If  it  have  a  depth  equal  to  J  of  its 
length,  and  a  form  of  section  as  strong  as  a  rectangular 
bar,  it  will  safely  sustain  1,000  to  l,2001bs.  to  the  inch  ; 
and  it  is  recommended  to  allow  one  inch  of  section  in 
each  end  cross-bar  to  every  l,000ft>s,  sustained  at  the 
joint.  Then,  there  being  two  cross  bars  together,  the 
point  will  be  doubly  secure. 

Semicircular  notches  in  the  ends  of  contiguous  arch 
pieces,  form  a  vertical  circular  hole  at  the  joint,  for  the 
passage  of  the  vertical  member. 

When  the  side  plates  are  thin,  the  thickness  should 

be  increased  for  a  few  inches  from  the  end,  to  afford  a 

FIG  28  suitable  bearing  surface  at  the  joint; 

r-pirv ' and  the  ends  of  arch  pieces  should 

I      I   flllll          Hj    be  fitted  (usually  by  planing),  to  a 

I  y    proper  bevel  to  form  a  fair  joint. 

The  joints,  however,  are  sometimes 

formed  by  cutting  taper  key  seats  (as  seen  in  Fig.  28), 


ARCH  TRUSS  BRIDGES. 


175 


in  one  of  the  contiguous  ends,  to  admit  wrought  iron 
wedges  about  an  inch  wide,  and  in  sufficient  number 
to  give  a  bearing  upon  wedges,  equal  to  at  least  one- 
half  the  section  of  iron  in  the  chord.  This  method  has 
answered  well  in  a  large  number  of  bridges,  and  is 
convenient  for  adjusting  the  arch  in  line;  but  the 
planed  ends  form  much  the  more  workmanlike  joint. 

The  centre  arch  piece  has  usually  a  full  top  plate 
over  the  whole  width  of  the  piece. 

The  endmost  section,  or  foot  piece  of  the  arch,  con 
nects  with  the  chord  by  means  of  horizontal  holes  in 
FlG   29  tf16'  ft'et  to  receive  the  ends 

of  an  o^en  end  iink  of  the 
chord,  which  is  secured  by 
screws  and  nuts  as  shown 
in  Fig.  29,  representing  an 
inside  view  of  the  foot  of 
one  branch  of  the  arch. 

C.  The  chord  is  composed  of  two  long  links  of  round 
or  square  iron  to  each  panel,  connected  by  cast  iivn 

connecting  blocks  at 
points  vertically  under 
the  arch  joints.  The 
form  of  these  blocks  is 
represented  in  F?g.  30. 
They  diminish  in  length 
from  the  endmost  to  the 
centremost,  the  former 
being  long  enough  to  re 
ceive  the  links  running  parallel  from  the  connection 
with  the  arch,  and  the  ne&t  block,  being  shorter  by 
twice  the  diameter  of  the  link  iron ;  the  ends  of  links 
toward  the  centre  of  the  truss,  going  next  the  ends  of 


FIG.  30. 


176  BRIDGE  BUILDING. 

connecting  blocks,  and  outside  of  the  ends  pointing 
toward  abutments  ;  and,  the  members  of  each  pair  of 
links  being  parallel  with  one  another.  [D,  Fig.  27.] 

The  connecting  block  has  an  oblong  section  where 
it  receives  the  links,  being  rounded  on  the  sides  to  tit 

the  semicircular  ends  of  links. 
Jbia.  30 A.  mi  ,      , ,  , 

I  here  should  be  an  accurate 

fit  between  these  parts,  to 
effect  which,  perhaps,  the  best 
plan  is  to  ream  the  ends  of 
links,  and  turn  the  bearings  of 
blocks  to  a  uniform  size.  For 
this  purpose,  the  block  is  cast  with  extra  metal  to  be 
turned  off  at  the  bearings,  and  with  the  portion  be 
tween  bearings  a  little  thinner  vertically,  than  the 
turned  portions,  as  shown  in  Fig.  30A,  in  which  a  is 
a  section  and  bb  are  the  bearing  surfaces. 

The  vertical  thickness  of  the  block  where  it  receives 
the  links,  should  be  at  least  1J  times  the  diameter  of 
the  link  iron,  and  the  cross-section  multiplied  by  the 
width  of  block,  and  divided  by  diameter  of  link  iron, 
should  give  a  quotient  about  13  times  as  great  as  the 
cross-section  of  both  sides  of  the  link. 

The  middle  portion  of  the  block  is  cast  with  the 
proper  size  and  form  for  the  upright  and  diagonal 
members  to  pass  through  in  the  required  directions, 
and  is  provided  with  suitable  facets  for  the  bearings  of 
nuts.  The  least  cross-section  through  all  or  any  of  the 
holes,  should  be  at  least  one-quarter  greater  than  the 
section  at  the  link  bearings.  In  Fig.  30,  «,  b  and  c  re 
spectively  represent  a  side,  end  and  top  view  of  the 
cast  iron  connecting  block. 

The  oblong  section  of  the  connecting  block  was 
adapted  to  obtain  greater  transverse  strength  in  the 


ARCH  TRUSS  BRIDGES.  177 

direction  of  the  strain.  But  it  has  recently  occurred 
to  the  author,  that  perhaps,  after  all,  a  circular  section 
of  block  would  have  the  advantage,  inasmuch  as  it 
would  not  require  so  short  a  bend  at  the  ends  of 
links ;  whence  they  could  the  better  adapt  thems  Ives 
to  the  block,  and  would  not  require  so  great  a  disturb 
ance  in  the  condition  of  fibres  or  particles  of  the  iron 
in  forming  the  bends.  With  a  diameter  of  block  equal 
to  3  times  that  of  the  link  iron  (in  case  of  round  iron), 
it  is  believed  that  good  iron  would  suffer  the  bend 
without  material  deterioration,  or  greater  liability  to 
break  the  ends,  than  in  other  parts  of  the  link,  espe 
cially  if  welded  in  the  straight  part. 

The  enlarged  central  portion  of  the  connecting  block 
has  upon  its  upper  side,  a  flat  surface  rising  a  little 
above  the  links,  to  afford  a  beam  seat  for  the  cross 
beams  of  the  bridge  to  rest  upon ;  which,  in  case  of 
wooden  beams,  should  present  a  bearing  surface  of  30 
to  40  square  inches. 

CL  The  upright  is  made  of  round  wrought  iron,  1  j 
to  2  inches  in  diameter,  for  bridges  from  60  to  100  feet 
in  length,  when  designed  for  common  road  purposes. 
The  upper  end  is  furnished  with  a  screw  nut,  and  a 
ring  or  collar  welded  on  at  a  sufficient  distance  below 
the  nut  to  allow  the  arch  castings,  and  eyes  of  dia 
gonals  to  come  between  nut  and  collar. 

The  lower  end  is  turned  or  swaged  down  to  a  dia 
meter  J  "  or  §  "  less  than  the  body  of  the  rod,  for  a 
length  sufficient  to  reach  through  the  connecting  block, 
and  receive  a  nut  on  the  end.  This  is  to  form  a 
shoulder  at  the  upper  side  of  the  block,  to  act  in  case 
of  a  thrust  action  of  the  tfpright. 


178  BRIDGE  BUILDING. 

The  two  longest  uprights  have  usually  been  made 
double  and  divergent  from  the  collar  downward,  the 
branches  being  of  iron  from  J"  to  f  "  smaller  in^ dia 
meter  than  the  single  uprights,  and  passing  through 
the  connecting  block  near  the  links,  either  inside  or 
outside,  as  deemed  most  appropriate,  with  a  thin  nut 
above,  and  a  common  nut  below  the  block  ;  also  a  cast 
iron  washer  above  the  upper  nuts,  for  the  beam  to  rest 
on,  instead  of  resting  upon  the  central  part  of  the 
block.  The  object  is  to  give  lateral  steadiness  to  the 
arch,  and  diminish  its  vibration. 

A  better  effect  in  the  same  direction  is  produced  by 
connecting  the  upper  ends  of  those  uprights  across 
from  truss  to  truss,  in  case  of  long  bridges.  For  this 
purpose,  the  upright  may  extend  a  little  above  the 
arch,  when  necessary  to  give  head-way  (or,  perhaps 
better  still,  the  arch  itself  might  rise  higher  above  the 
chord,  thus  diminishing  the  action  upon  both  arch  and 
chord),  and  a  light  cast  or  wrought  iron  strut  intro 
duced,  to  counteract  the  tendency  to  vibration  of  the 
arches,  arising  from  the  spring  of  the  beams.  As  the 
the  two  trusses  naturally  tend  to  vibrate  in  opposition 
to  each  other,  it  is  suggested  whether  simple  ties  of 
f "  iron,  would  not  so  break  the  regularities  of  the 
vibrations  Cis  to  prevent  their  increase  to  an  objection 
able  extent.  The  rigid  strut,  however,  would  be  more 
effective,  being  capable  of  acting  in  both  directions ; 
and,  if  thrown  into  the  form  of  a  graceful  arch,  it 
would  be  ornamental  withal. 

GIL  The  diagonals  are  round  rods,  with  an  eye  at 
the  upper,  and  a  screw  and  nut  at  the  lower  end  of 
each  ;  the  screw  portion  being  about  J"  larger  in  dia 
meter  than  the  plain  part  of  the  rod.  Tsvo  eyes  of 


ARCH  TRUSS  BRIDGES.  179 

diagonals  go  upon  each  upright  (except  the  endraost) ; 
that  of  the  rod  running  downward  toward  the  centre 
going  above  the  other,  the  better  to  prevent  interfer 
ence  with  the  cross-bars  of  arch  pieces,  as  will  be  un 
derstood  by  reference  to  C,  Fig.  27. 

The  eyes  He  in  horizontal  positions,  the  rod  in  each 
case  being  bent  to  the  required  pitch  to  meet  the  con 
necting  block.  The  bend  should  be  as  near  as  may  be 
to  the  eye,  without  preventing  a  fair  bearing  of  the  eye 
upon  the  collar,  or  the  subjacent  eye.  Care  should  be 
taken  to  have  fullness  and  strength  in  the  neck  of  the 
eye,  that  it  may  withstand  the  indirect  strain  at  that 
point. 

The  proper  sizes  for  diagonals  and  chords  should  be 
such,  in  common  road  and  street  bridges,  as  to  afford 
at  least  one  square  inch  of  cross-section  for  each 
15,0001bs.  of  stress  produced  by  the  greatest  load  to 
which  such  bridges  are  liable,  which  in  the  author's 
opinion,  should  be  estimated  at  about  lOOIbs.  to  each 
square  foot  of  bridge  flooring,  exclusive  of  weight  of 
structure  ;  a  rule  which  he  originally  adopted,  and  has 
adhered  to  in  practice  with  most  satisfactory  results. 
Many  bridges  have  been  constructed  with  lighter  pro 
portions  than  this  rule  would  require,  some  of  which 
have  endured,  while  others  have  failed. 

It  is  true  that  ordinary  road  bridges  are  seldom  ex 
posed  to  lOOfbs.  to  the  foot  of  floor  surface,  but  it  is 
nevertheless,  deemed  expedient  to  provide  for  such 
a  contingency. 

The  modes  of  estimating  stresses  of  different  parts 
of  the  truss,  have  been  fully  discussed  in  preceding 
pages,  [xxvn  &c.],  and  it  seems  unnecessary  in  this 
place,  to  specify  more  particularly  the  dimensions  of 
the  several  members  of  the  truss. 


180 


BRIDGE  BUILDIXG. 


FIG.  SOB. 


CIII.  Another  devise  for  the  connections  of  diagonals 
at  the  arch,  is  to  replace  the  bent  .eye  of  the  diagonal 

by  a  straight  end  with  screw 
and  nut,  and  to  have  oblique 
holes  cast  in  the  ends  of  arch 
pieces  for  diagonals  to  pass 
through,  on  each  side  of  the 
upright.  [See  Fig.  30B]. 
The  diagonals  may  be  single, 
or  in  pairs.  The  latter  plan 
is  preferable,  as  giving  a 
better  balanced  action  ;  es 
pecially  in  case  of  rail  road  bridges,  which  are  subject 
to  greater  action  upon  diagonals.  This  plan  obviates 
a  degree  of  lateral  strain  upon  uprights,  resulting  from 
the  eye  connection.  In  this  case,  the  upright  should 
have  a  shoulder  bearing  on  the  under  side  of  arch 

O 

castings,  to  sustain  the  thrust  action. 

CIV.  It  will  be  seen  that  these  trusses,  having  a 
width  of  base  equal  to  about  one-fourth  of  the  height, 
will  support  themselves  laterally,  without  any  assist 
ance  from  one  another,  or  from  other  parts  of  the 
structure,  wherefore  the  flooring,  including  cross 
beams,  may  be  entirely  of  wood,  and  may  be  renewed 
at  pleasure,  without  any  disturbance  of  the  iron  work  ; 
a  property  peculiar  to  this  kind  of  truss. 

The  original  design,  therefore,  was  to  use  wooden 
cross-beams,  formed  in  two  pieces,  as  by  slitting  an  or 
dinary  beam  vertically,  bolting  the  parts  together,  and 
boring  at  the  ends  for  the  uprights,  so  that  they  may  be 
conveniently  put  in  and  removed  whenever  they  re 
quire  renewal.  Diagonal  braces  of  wood,  or  what  is 
much  better,  tie  rods  of  iron  with  an  eye  at  each  end, 


ARCH  TRUSS  BRIDGES.  '  181 

and  a  swivel  or  turn  buckle  adjustment  near  one  end, 
a  pair  between  each  two  consecutive  beams,  to  which 
they  are  bolted  near  the  uprights,  are  required  to  pre 
vent  a  lateral  swinging  or  swaying  of  the  bridge ; 
whence  these  members  are  usually  called  sway  braces, 
or  sway  rods.  In  the  end  panels  the  sway  rods  are 
attached  to  the  feet  of  the  arch. 

Upon  the  cross-beams,  longitudinal  joists  are  placed 
to  support  the  floor  plank,  a  thing  so  simple,  and  so 
generally  understood  as  to  require  no  further  descrip 
tion  or  illustration  in  this  place.  More  or  less  casings 
and  finishings  of  wood  work  outside  of  the  road  way, 
are  usually  added,  according  to  circumstances,  or  the 
taste  of  the  builder. 

CV.  The  rise  of  the  arch  above  the  chord,  will  admit 
3f  a  considerable  degree  of  variation.  A  pitch  of  24 
to  26  degrees  for  the  end  arch  pieces,  it  will  seldom  be 
advisable  to  exceed  in  either  direction.  That  pitch 
divided  by  the  whole  number  of  joints  in  the  arch  (6, 
for  a  seven  panel  truss),  gives  the  angle  of  deflection 
at  the  joint,  equal,  of  course,  to  twice  the  angle  of  bevel 
for  ends  of  arch  pieces. 

This,  however,  does  not  produce  an  arch  in  equili- 
brio  under  a  uniform  load,  which,  as  we  have  seen, 
[xxvn  and  LII]  requires  a  parabolic  curve,  while  equal 
deflections  produce  a  curve  between  the  parabola  and 
the  circular  arc;  not  departing  from  the  former,  how 
ever,  widely  enough  to  be  of  material  moment  for  or 
dinary  spans.  The  effect  is  only  the  throwing  of  a 
trifle  more  action  upon  certain  diagonals ;  for  which 
the  convenience  of  uniform  bevels,  is,  perhaps,  an  ade 
quate  offset. 


182  BRIDGE  BUILDING. 


CYLINDRICAL  ARCHES. 

CYI.  Arch  Truss  bridges  have  been  constructed 
with  cylindrical  arch  castings,  in  connection  with  up 
rights,  dividing  and  diverging  downward  from  the 
arch  to  the  beams,  thus  serving  to  give  lateral  support 
to  the  arch,  and  preserve  it  in  line. 

This  form  of  arch  castings  was  supposed  at  one  time, 
to  possess  sufficient  advantage  over  that  already  before 
described,  and  which  is  commonly  known  as  the  In 
dependent  Arch,  to  warrant  its  adoption,  inasmuch  as 
it  is  the  stronger  form  to  withstand  compressive  strain. 
But  it  is  also  more  expensive  in  the  manufacture,  to 
an  extent  perhaps  sufficient  to  balance  any  practicable 
saving  in  weight  of  metal.  Hence,  the  Independent 
Arch  has  acquired  decidedly  the  greater  popularity,  to 
which  its  just  title  can  scarcely  be  questioned.  Further 
detail,  therefore,  as  to  the  mode  of  constructing  the 
cylindrical  arch  bridge  will  not  be  here  recited. 

IRON  BEAMS  FOR  BRIDGES. 

CVII.  It  is  now  over  thirty  years  since  the  writer's 
attention  was  first  directed  to  the  subject  of  Iron  Truss 
Bridges  ;  a  period  which  may  be  said  to  comprise  the 
history  of  the  use  of  iron  as  the  sole  or  principal  mate 
rial  in  the  main  supporting  members  of  those  useful 
structures. 

At  that  time,  there  was  one  Iron  Truss  Bridge  in  use 
in  the  state  of  New  York,  and  only  one,  to  the  writer's 
knowledge,  either  in  this  state,  or  in  the  world,  though 
the  fact  may  be  otherwise. 

That  bridge,  though  possessing  merit  as  the  result 
of  a  first  effort,  did  not  prove  a  complete  success,  hav- 


ARCH  TRUSS  BRIDGES.  183 

ing  failed,  and,  being  rebuilt,  failed  a  second  time, 
many  years  ago;  so  that,  at  the  present  time,  a  certain 
Iron  Truss  Bridge  built  by  the  author  of  this  work  in 
1841  and  42,  upon  the  Arch  Truss  plan,  essentially  as 
described  in  the  last  few  preceding  pages,  is  believed  to 
be  the  oldest  Iron  Truss  bridge  in  use  in  this  country, 
if  not  in  the  world. 

At  that  time,  it  was  not  thought  advisable  to  attempt 
more  than  the  construction  of  Iron  Trusses,  to  be  used 
in  connection  with  wooden,  beams,  joist,  &c.  ;  which 
latter  portions  could  be  renewed  as  required,  with 
comparatively  little  trouble,  and  at  much  less  cost, 
than  the  interest  upon  the  extra  expense  of  iron  beams 
would  amount  to  within  the  lifetime  of  wooden  beams. 
But  as  the  public  mind  seems  now  to  have  become 
convinced,  not  only  of  the  safety  and  expediency  of 
the  use  of  iron  for  the  trusses,  but  also  for  the  beams 
of  bridges,  it  becomes  a  question  of  interest  to  deter 
mine  the  best  manner  of  constructing  and  inserting 
such  beams. 

CYIII.  Four  general  plans  of  iron  beams  have  been 
used  successfully ;  namely,  the  cast  iron  web  and 
flange  beam,  the  wrought  iron  skeleton,  the  composite 
(wrought  and  cast  iron),  and  the  solid  wrougth  iron 
rolled  web  and  flange,  or  I  beam.  These  may  all  be 
used  with  good  results,  in  particular  cases,  and  under 
modifications  adapted  to  respective  circumstances. 

For  general  use,  however,  I  regard  the  solid -rolled 
I  beam  as  entitled  to  a  decided  preference ;  and,  with 
out  discussing  relative  merits  in  this  place,  I  propose 
simply,  at  this  time,  to  suggest  plans  for  adapting  the 
last  named  beam  to  the  Whipple  Arch  Truss,  thus 
making  the  plan  about  all  that  can  be  hoped  to  be  at- 


184 


BRIDGE  BUILDING. 


tairied,  as  a  cheap,  substantial  and  durable  iron  bridge 
for  general  use,  for  spans  varying  from  40  to,  —  perhaps 
125  feet. 

For  bridges  16  to  18  feet  wide  in  the  clear,  and 
panels  ten  or  eleven  feet  long,  a  9  inch  beam,  weighing 
30Bbs.  to  the  foot,  is  in  good  proportion  ;  and  when 
side  walks  are  not  required,  the  beams  may  be  cut 
with  square  ends,  just  long  enough  to  go  between  the 
uprights  of  opposite  trusses,  and  provided  with  a  fixture 
at  each  end,  formed  of  a  plate  of  iron  about  f"  thick, 
7"  wide,  and  about  2'  long,  bent  in  the  form  of  a  jews- 
harp  bow.  The  loop,  or  bow  (w,  Fig.  31),  is  to  encir- 

FIG.  31. 


cle  the  upright,  and  the  straight  sides,  to  receive  the 
vertical  web  of  the  beam  between  them,  and  to  be 
fastened  thereto,  by  two  bolts  and  nuts.  One  of  these 
should  be  1J"  in  diameter,  and  long  enough  to  receive 
the  eye  of  a  lateral  diagonal  tie,  or  sway  rod  (to  prevent 
swaying  or  swinging),  under  both  head  and  nut,  and 
placed  about  5|"  from  end  of  beam,  and  2J"  above 
lower  edge  of  plate.  The  other  bolt  may  be  1J"  or 
1J",  and  placed  with  its  centre  1J"  from  end  of  beam, 
arid  from  upper  edge  of  plate.  The  thread  of  the  screw 


ARCH  TRUSS  BRIDGES. 


185 


should  not  run  into  the  plate,   even  if  a  washer  be  re 
quired  in  order  to  fetch  the  work  together. 

A  convenient  modification  of  this  fixture  is  to  have 
it  made  in  two  pieces  with  two  f"  bolts  outside  of 
the  upright,  as  seen  at  c,  Fig.  32.  This  affords  a  con- 

Fia.  32. 


venient  means  of  attaching  a  light  bracket  (6),  to  sus 
tain  face  plank  and  coping  (a),  over  the  chords,  such 
as  are  commonly  used  in  this  kind  of  bridge.  It  also 
enables  iron  beams  to  be  inserted  in  bridges  originally 
built  with  wooden  beams. 

The  connecting  block  in  this  case,  should  have  an 
elevated  ring  around  the  upright,  for  the  eye  of  the 
fixture  to  bear  upon,  to  keep  the  beam  from  bearing 
altogether  upon  the  inside  of  the  upright,  and  produc 
ing  unequal  strain. 

CIX.  Another  suggestion  is,  to  form  a  stirrup  in  the 
upright  just  above  the  connecting  block  for  the  beam 
to  pass  through  and  rest  in  :  as  seen  at  6,  Fig.  31.  This 
will  admit  of  projecting  beams  to  support  side  walks. 

The  stirrup  may  be  formed  of  iron  1"  by  2"  or  2J", 
according  to  the  character  of  bridge.  The  iron  should 
24 


186  BRIDGE  BUILDING. 

be  upset,  so  as  to  give  sufficient  width  and  strength  at 
the  bottom  of  the  stirrup  to  allow  a  1J"  stem  to  be 
screwed  in,  to  pass  through  and  support  the  connecting 
block.  This  stem  may  extend  above  the  bottom  of  the 
stirrup,  about  •§",  a  hole  being  made  in  the  under  side 
of  the  beam  to  receive  that  projection.  The  thread  of 
the  projecting  part  of  the  screw,  which  enters  the  beam, 
should  be  turned  or  chipped  off.  This  plan  may  be 
used  in  bridges  either  with  or  without  side  walks. 

Again,  the  upright  may  terminate  in  a  flange  at  the 
top  of  the  beam,  and  bolts  screwed  or  cast  in  the  top 
of  the  block,  or  running  through  the  block  with  head 
or  nut  below,  one  on  each  side  of  the  beam,  and  con 
necting  with  the  flange  of  the  upright,  as  shown  at  B, 
Fig.  32. 

In  the  case  of  double  uprights,  the  beam  being  cut 
to  go  between  the  inner  branches,  the  fixture  plates 
should  lap  about  20"  upon  the  beam,  and  extend  so  as 
to  clasp  both  branches  of  the  upright. 

CX.  To  introduce  the  solid  wrought  beam  in  bridges 
with  sidewalks  originally  constructed  for  wooden  beams, 
the  following  plan  is  suggested. 

Let  the  beam  be  cut,  say  1"  shorter  than  the  space 
between  opposite  uprights.  Then,  take  for  each  end 

FIG.  33. 
.p 

!  ni>     ^»— 


of  the  beam,  two  plates  J"  thick  and  7J"  wide,  or, 
wide  enough  to  fill  the  space  between  the  flanges  of 


ARCH  TRUSS  BRIDGES.  187 

the  beam  at  V  from  the  centre,  so  that  one  being 
placed  on  each  side,  they  will  be  kept  far  enough 
apart  to  admit  the  upright  between  them.  The  plates 
should  be  long  enough  to  lap  20"  upon  the  beam,  and 
extend  to  outside  of  side  walk.  They  may  be  bolted 
with  two  V  bolts  near  the  end  of  the  lap,  and  one  near 
the  end  of  the  beam  by  the  upright;  as  seen  under  the 
letter  u  in  Fig.  33.  A  1 J"  bolt  in  the  centre  of  depth, 
and  7  or  8  inches  from  the  upright,  will  serve  both  to 
aid  in  holding  the  plates  in  place,  and  to  connect  the 
sway  rods  I.  These  plates  should  not  be  cut  by  bolt 
or  rivet  holes  in  the  upper  part,  except  at  considerable 
distance  from  the  upright  u. 

Small  bolts  or  rivets,  r  r,  etc.,  should  be  inserted  at 
intervals  of  9  or  10  inches,  near  the  lower  edge,  with 
thimbles  to  stay  the  extension  plates  apart, 
leaving  a  space  equal  to  the  diameter  of  the 
upright.  In  Fig.  33,  s-w  is  a  part  of  the 
extension  for  supporting  side  walk ;  s,  a 
cast  iron  saddle  weighing  about  4Sbs.  for 
joist  bearings,  and  c,  a  cross-section  through 
the  splice. 

To  afford  a  proper  bearing  upon  the  con 
necting  block,  it  is  proposed  to  use  a 
wrought  iron  ring  (R.  Fig.  34),  high 
^>xl  enough  to  throw  the  whole  weight  upon 
the  extension  plates  ee,  and  f"  to  V  in 
width,  except  on  the  side  next  the  beam  proper,  where 
it  is  to  be  clipped  or  drawn  down  to  J".  This,  how 
ever,  is  not  an  essential  point.  In  case  of  bridges 
already  erected,  the  ring  will  have  to  be  left  open  as 
at  R',  and  when  used,  heated  and  closed  around  the 
upright. 


188  BRIDGE  BUILDING. 

CXI.  The  Link  Chord,  composed  of  a  set  of  links 
to  each  panel,  connected  by  pins  or  connecting  blocks 
(the  latter  affording  also  points  of  attachment  for  ver 
ticals,  diagonals,  &c.),  both  for  Arch  and  Trapezoidal 
trusses,  was  originally  adopted  by  the  author,  as  the 
readiest  means  of  putting  the  requisite  amount  of  chord 
material  in  a  manageable  form,  both  as  it  regards  manu 
facturing  the  parts,  and  erecting  the  structure.  This 
form  renders  the  whole  section  available  for  sustaining 
tension,  avoiding  any  loss  in  rivet  or  bolt  holes  for 
forming  connections. 

The  experience  of  more  than  a  quarter  of  a  century, 
during  which  time  many  hundreds  of  bridges  with  link 
chords  have  been  constructed,  and  used  in  almost  all 
conceivable  conditions,  (in  many  cases,  undoubtedly, 
the  links  having  been  but  imperfectly  manufactured 
and  fitted  to  the  connecting  blocks),  with  a  degree  of 
success  and  satisfaction  seldom  exceeded,  may  reasona 
bly  be  regarded  as  fairly  establishing  the  efficiency  and 
safety  of  this  mode  of  construction,  when  proper  care 
is  used  in  the  performance  of  the  work. 

Continued  and  successful  usage  in  a  multitude  of 
instances,  is  regarded  as  a  better  criterion  as  to  the 
reliability  of  a  plan  of  construction,  than  a  small  num 
ber  of  isolated  tests,  however  severe ;  and  such  usage 
the  link  chord  has  been  subjected  to. 

CXII.  The  theoretical  questions  to  be  considered  in 
this  case,  would  seem  to  be,  as  to  the  possible  deteriora 
tion  of  the  cohesive  strength  of  the  iron,  produced  in 
forming  the  bends  at  the  ends  of  links —  the  indirect, 
or  lateral  strain  in  those  parts,  resulting  from  imper 
fection  of  the  fitting  to  the  connecting  block  or  pin, 
and,  the  imperfection  of  the  weldings,  both  as  it  re- 


ARCH  TRUSS  BRIDGES.  189 

gards  complete  cohesion,  and  the  tendency  to  crystalli 
zation  under  the  welding  heat,  not  being  fully  destroyed 
by  subsequent  hammering  and  working. 

The  whole  process  of  the  manufacture  and  refinement 
of  iron,  is  based  upon  the  principle  that  disconnected 
pieces  of  iron  brought  in  contact  under' intense  heat, 
but  without  complete  fusion,  and  subjected  to  violent 
compression,  as  by  hammering  or  rolling,  will  unite, 
and  become  a  single  piece  or  mass. 

Every  bar  of  refined  iron  found  in  the  iron  market, 
is  composed  of  half  a  dozen  or  more  parts,  which  were 
once  separate  and  disconnected.  Those  having  been 
"  fagoted,"  or  placed  in  juxtaposition,  and  submitted 
to  a  welding  heat,  and  passed  repeatedly  between 
ponderous  rollers,  or  subjected  to  the  blows  of  heavy 
hammers,  are  united  and  drawn  into  bars  of  required 
sizes  and  forms  for  use. 

These  masses,  taken  from  the  furnace  and  suffered 
to  cool  without  hammering  or  rolling,  would  be  found 
more  or  less  crystaline  and  brittle.  But  the  latter 
operations  prevent  such  a  result,  and  the  iron  becomes 
more  or  less  soft  and  flexible,  even  in  a  cold  state. 

Iron  which  has  undergone  the  uniform  process  of 
rolling,  is  generally  of  uniform  quality  and  strength 
throughout  the  whole  piece  ;  and,  as  far  as  it  can  be 
used  in  that  state,  without  re-heating  and  re-working, 
it  may  be  regarded  as  somewhat  more  reliable  than 
when  it  has  been  forged  and  welded  into  different  and 
more  complex  forms. . 

The  high  temperature  required  in  welding,  demands 
experience  and  judgment  in  determining  the  proper 
time  to  "  strike,"  that  is,  when  the  metal  is  hot  enough 
to  adhere  firmly,  but  not  overheated  to  burning. 
Moreover,  though  the  hammering  required  to  bring 


190  BRIDGE  BUILDING. 

the  parts  together  and  reduce  them  to  proper  form  and 
size,  may  prevent  crystalization  immediately  at  the 
welded  point,  still  on  either  side  are  portions  which 
may  have  "been  heated  so  as  to  change  the  arrange 
ment  of  particles,  and  not  subjected  to  sufficient  ham 
mering  to  counteract  the  deteriorating  tendency. 
Hence,  a  break  is  more  liable  to  take  place  a  little  on 
one  side,  than  immediately  through  the  welded  part. 

To  obviate  this  liability,  the  parts  to  be  welded  should 
be  enlarged  by  upsetting  several  inches  from  the  end, 
so  as  to  admit  of  re-drawing  under  the  hammer  a  little 
beyond  where  the  intense  heat  has  reached. 

But  theory  aside  for  the  moment,  although  the 
avoidance  of  welding  in  work  to  be  exposed  to  great 
stress  is  desirable,  it  is  nevertheless  a  fact  established 
by  large  experience,  that  welded  parts  will  bear  as 
great  a  strain  as  takes  place  in  well  proportioned 
bridge  work,  with  as  much  certainty  as  ever  has  been 
realized  in  any  department  of  the  means  of  locomotion. 

Danger  lurks  everywhere  at  all  times.  In  railroad 
travel,  boilers  burst,  rails  break,  wheels  and  axles 
break,  etc.,  etc.,  but  the  failure  of  a  weld  in  bridge 
work  is  rare  indeed,  and  very  few  authenticated  cases 
can  be  referred  to. 

I  would,  however,  prefer  a  weld  in  the  straight  part 
rather  than  in  the  end  of  a  link,  unless  made  with  an 
excess  of  section  around  the  bend.  "Whether  a  bend 
around  a  pin  of  1J  or  2  times  the  diameter  of  the  link 
iron  is  more  liable  to  break  than  the  straight  sides  of 
the  link,  I  can  refer  to  no  reliable  authority  to  deter 
mine.  The  longitudinal  strain  is  no  greater  in  the 
bended,  than  in  the  straight  parts,  if  well  fitted  to  the 
pin.  But  of  course,  it  can  not  be  expected  to  have  a 
fit  so  close  as  to  ensure  a  firm  pressure  quite  round  the 


ARCH  TRUSS  BRIDGES.  191 

semi-circle.  Hence  the  bearing  is  mainly  on  the  back 
Bide  of  the  pin,  until  by  a  yielding  to  compression,  and 
by  a  slight  bending  of  the  link  end,  a  pressure  is  pro 
duced  all  around. 

This  slight  bending,  good  iron  will  undergo  without 
having  it?  strength  impaired,  when  in  its  normal  con 
dition.  But  this  condition  is  disturbed  in  the  process 
of  bending,  the  outside  portion  being  extended,  and 
the  inside  compressed,  whereby  the  stiffness  of  the  part 
is  increased.  In  the  outside  portion  the  power  of  re 
sisting  extension  is  increased,  while  that  of  the  inside 
portion  is  possibly  diminished ;  and,  whether  the 
aggregate  resistance  to  extension  is  increased  or  dimin 
ished,  experiment  alone  can  determine  ;  and,  undoubt 
edly,  the  more  soft  and  flexible  the  iron,  the  better  can 
it  adapt  itself  to  a  bearing  upon  the  pin.  Hence,  it 
should  be  allowed  to  cool  gradually  from  a  full  red 
heat,  after  the  shaping  is  finished. 

Hence,  also,  the  necessity  of  extra  section  in  welded 
ends,  which,  being  less  flexible,  must  obtain  bearing 
surface  by  compression  and  yielding  of  contiguous 
parts,  rather  than  by  bending,  and  consequently,  must 
undergo  greater  transverse  strain  in  the  end  of  the  link. 

CXIII.  A  link  formed  of  wire  J"in  diameter,  formed 
to  a  pin  /j"  in  diameter  at  one  end,  and  brazed  with 
a  long  lap  at  the  other,  suffered  a  permanent  stretch 
in  the  straight  part,  of  one  per  0.  of  its  length,  with  no 
apparent  injury  at  the  ends.  Other  analogous  experi 
ments  have  shown  similar  results,  namely,  that  the 
straight  portions  will  yield  before  the  bended  portions. 

Now  the  same  degree  of  disturbance  in  the  metal 
takes  place  in  a  small,  as  in  a  large  rod,  bent  to  a 
curve  whose  radius  has  the  same  ratio  to  the  diameter 


192  BRIDGE  BUILDING. 

of  the  rod.  Hence,  it  is  difficult  to  avoid  the  conclu 
sion  that  rods  of  soft  and  flexible  iron,  such  as  ought 
to  be  used  for  tension  members  in  bridge  work,  bent 
to  a  proper  fit  upon  connecting  pins  of  diameter  about 
twice  that  of  the  rods,  and  formed  into  links  by  weld 
ing  in  the  straight  parts,  are  quite  safe  under  any  stress 
within  the  limits  adopted  in  bridge  work. 

But  it  seems  to  be  more  convenient  to  form  the  weld 
at  one  end  of  the  link,  if  not  both,  and  such  has  been 
the  usual  practice;  and,  as  before  remarked,  if  a  sur 
plus  of  metal  section  quite  around  the  bend  be  secured, 
and  the  work  well  performed,  this  plan  can  scarcely  be 
regarded  as  faulty,  especially,  in  view  of  the  long, 
varied,  and  successful  usage  of  such  vast  numbers  of 
links  made  in  this  manner. 

Now,  although  the  link  chord  is  very  simple,  effi 
cient,  and  convenient  to  make  and  manage,  there  are 
available  alternative  devices,  some  of  which  will  be 
here  described. 

THE  EYE-BAR  CHORD. 

CXIY.  This  is  composed  of  two  or  more  single  rods, 
of  oblong,  square,  or  round  section  to  each  panel ; 
connected  by  cylindrical  pins  passing  through  strong 
eyes  at  each  end  of  the  chord  bars. 

This  plan  until  recently,  has  involved  quite  as  much 
welding  as  the  link  chord;  the  eyes  having  been 
formed  in  separate  pieces,  and  welded  to  the  body  of 
the  rod.  But  within  a  few  years  a  process  has  been 
devised  by  the  Phoenix  Iron  Co.,  of  Pennsylvania,  for 
upsetting  and  forming  eyes  upon  rolled  bars.  A  mold 
or  die  gives  the  desired  form  and  size  to  the  head,  and 
aside  from  the  fact  that  a  violent  disturbance  of  the 
normal  condition  of  the  iron  is  produced  in  the  vicinity 


ARCH  TRUSS  BRIDGES.  193 

of  the  bead,  there  can  be  no  question  as  to  the  excel 
lence  of  the  work  produced  ;  and  it  is  undoubtedly, 
perfectly  reliable,  under  any  stress  to  which  it  is  ad 
missible  to  expose  the  material  in  bridge  work. 

Figure  SOB  represents  the  joint  of  an  eye-plate  chord 
at  Cj  adapted  to  the  arch  truss.  Upright  and  diagonals 
have  each  an  eye  to  receive  the  connecting  pin  at  the 
lower  end.  The  upright  has  a  washer  above  the  eye 
to  form  a  beam  seat  above  the  eyes  of  the  chord  plates. 
Perhaps  the  washer  should  be  in  the  form  of  a  saddle 
or  stool,  with  downward  projections  bearing  upon  the 
pin  outside  of  the  diagonals  ;  or,  perhaps  inside,  in 
case  the  diagonals  be  in  pairs,  as  before  suggested. 
[cm.] 

SIZE  OF  CONNECTING  PIN. 

CXV.  Considering  the  average  bearing  upon  the 
pin,  to  be  at  the  centre  of  thickness  of  the  eye,  or  link 
end,  as  the  case  may  be,  the  thickness  of  the  eye  indi 
cates  the  leverage  upon  which  opposite  links  act,  when 
side  by  side  upon  either  end  of  the  pin.  Estimating 
the  strength  of  the  pin,  then,  at  4,500ft>s.  to  the  square 
inch  of  section,  with  a  leverage  equal  to  the  diameter 
of  the  pin  [see  xcvm,]  we  obtain  the  proper  diameter 
of  the  pin  as  follows  : 

Let  a=area  of  section  in  link  or  chord  bar. 
tf=thickness  of  eye=leverage  of  action. 
2=*=diameter  of  pin,  in  inches. 

Then,  .7854x2=area  of  pin  section  ;  and  this  multi 
3534.30 


plied  by  4,500  -|,=         .^  equal  to  tbe  resigtjng  p0wer 

of  the  pin  ;  while  15,000a=the  power  of  the  link  ;  and 
putting  these  two  expressions  equal  to  one  another, 
and  deducing  the  value  of  #,  we  have  the  required 
diameter  of  the  pin,  ^4.244a.*  inches,  =x. 
25 


194  BRIDGE  BUILDING. 

CXYI.  If  #=4  square  inches,  and  £=«1.5  inches, 
then  a.t  =  6,  and  x  =  ^6x4.244  =  2.94  inches. 
This  diameter  of  pin  is  required  to  withstand  the  action 
of  the  chord  alone,  which  is  the  only  stress  upon  the 
pin  when  the  chord  is  at  maximum  tension.  But 
when  the  diagonals  running  in  the  same  direction 
horizontally,  with  the  inside  links,  are  brought  into 
action,  they  act  in  conjunction  with  the  links  in  pro 
ducing  stress  on  the  pin. 

Now,  the  greatest  stress  upon  bn,  Fig.  11  [see  xxxiv] 
occurs  when  the  point  b  alone  is  loaded,  and  the  links 
ab  sustain  f  of  their  maximum  stress  from  movable 
load,  and  bn.  sustains  5wff,  giving  a  horizontal  pull  of  about 
6  5u>",  the  amount  varying  with  depth  of  truss.  Again, 
besides  the  6w"  bearing  at  the  point  «,  in  virtue  of 
the  movable  weight  (10),  at  6,  we  have  3w'  due  to  weight 
of  structure,  also  bearing  at  a  ;  and  assuming  &w'.  to 
be  equal  to  li£,  or  7w"  the  whole  pressure  at  a,  equals 
13i0",  when  the  horizontal  pull  of  bn  equals  6.5w". 

The  tension  of  ab,  in  the  usual  proportion  of  arch 
trusses,  equals  about  2J  times  the  bearing  at  a,  whence 
the  stress  of  ab  with  the  point  b  alone  under  load, 
equals  13^"x2.25*  =  29.25u>".  Deducting  from  this, 
6.610"  for  horizontal  pull  of  bn,  it  leaves  22.75w"  = 
stress  of  be.  Then,  assuming  the  diagonal  to  act  in 
the  centre  of  the  pin,  and  the  length  of  pin  between 
centres  of  bearing  of  outside  links  to  be  27",  we  find 
the  stress  at  the  centre  of  the  pin,  by  taking  the  mo 
ments  with  respect  to  the  centre,  of  the  action  of  the 
two  links  at  either  end  of  the  pin.  The  difference  of 
these  moments,  the  forces  being  opposite,  is  the  mo 
ment  of  the  force  producing  stress  at  the  centre  of  the 
pin;  in  other  words,  it  is  the  force  acting  transversely 


ARCH  TRUSS  BRIDGES.  195 

upon  the  pin,  at  a  leverage  of  1  inch,  the  inch  being 
our  unit  of  length. 

"We  found  the  pull  of  ab  =  29.25io",  or  14.625^"  at 
each  end  of  the  pin,  which  multiplied  by  distance  from 
centre  (13.5")  gives  a  moment  =  197.4375*//',  while  for 
be,  the  moment  is  JX22.75X12"  =  136.500"  ;  and  the 
difference  =  60.9375w"  =  stress  in  centre  of  pin,  upon 
a  leverage  of  I". 

Assigning  such  a  value  to  w"  as  will  give  the  as 
sumed  stress  of  15,0001fes.  to  the  inch  upon  ab  with  the 
truss  fully  loaded,  with  a  bearing  at  a,  of  2lw"  for  mova 
ble,  and  lw"  (=  3*0'),  of  weight  of  structure,  we  find  a 
stress  of  28  x  2  J  (—  63)z0"  =  8  X  15,0000ft>s.  =  120,000ft>s ; 
whence  w"  =  l,905Ibs.  which,  being  substituted  in  the 
above  amount  of  60.9375*0"  gives  the  stress  in  pounds 
at  the  centre  of  the  pin,  on  a  leverage  of  1",  equal  to 
116,086Ibs. 

We  have  seen  [xcvin]  that  the  resisting  power  of 
a  projecting  pin  equals  4,500—,  which  in  this  case,  equals 
4,500AD  (L  being  =  1),  equal  to  4,500  X.7854X3.  Then, 
making  this  expression  =  116,088ft>s.  we  have  x  =  3.2"  ; 
being  0.26"  larger  than  is  required*  to  withstand  the 
action  of  chord  alone,  at  its  maximum  stress,  as  already 
shown  [cxvi.]. 

By  similar  process  we  find  very  nearly  the  same  re 
sults  with  respect  to  the  shorter  pins  toward  the  centre 
of  the  truss.  For,  although  the  maximum  action  of 
diagonals  takes  place  under  greater  stress  upon  chords, 
the  difference  is  balanced  by  diminution  in  length  of 
pins  toward  the  centre  of  the  truss. 

Should  this  mode  of  connection  be  adopted,  the  pre 
ceding  illustrations  and  examples,  it  is  hoped,  will 
enable  the  proper  proportions  of  connecting  pins  to  be 
determined  for  trusses  of  whatever  dimensions. 


196  BRIDGE  BUILDING. 

A  RIVETED  PLATE-CHORD. 

CXVII.  May  be  formed  of  Hat  plates  as  long  as  may 
be  conveniently  managed,  connected  by  splicing  plates 
of  a  little  more  than  half  the  thickness  of  the  chord 
plates,  one  upon  each  side,  riveted  or  bolted  with  such 
a  distribution  of  rivets,  &c.,  as  may  not  weaken  the 
plates  by  more  than  the  width  of  one  rivet  hole. 

The  area  of  rivet  section  should  be  at  least  f  to  f  as 
great  as  the  net  section  of  the  chord  plate,  on  each  side 
of  the  joint;  and,  go,  Fig.  34J  denoting  the  splicing 
plate,  the  distance  cd,  from  the  joint  to  the  centre  of 
the  first  rivet  hole,  should  be  at  least  twice  the  diame 
ter  of  the  rivet  (depending  somewhat  upon  the  size  of 
rivet  and  thickness  of  plate,  as  well  as  the  soundness 
of  grain  in  the  iron).  The  succeeding  rivets,  a,  £,/, 
&c.,  should  be  placed  alternately  on  opposite  sides  of 
the  centre,  so  that  the  oblique  distance  ac  (==  0),  may 
equal  the  transverse  distance  (=  T),  +  the  diameter 
of  whole  (=  II  ).  Then,  representing  the  longitu 
dinal  distance  be,  by  L,  we  have  T+H  =  0,  and 
(T+H)2  =  O2,  -  T2+L2  =  T24-2TH-fII2;  whence  L 
=  \/2T.H  +  II2. 

If  the  plates  be  6"  wide,  and  T  =  3J"  (which  is  re 
garded  as  in  good  proportion,  the  above  formula  gives 
L  ==  2J"  very  nearly,  for  a  f "  hole.  Then,  5"  being 
allowed  for  the  space  ce,  and  2"  each  for  cd  and  eg,  the 
splice  plates  would  have  a  length  of  20J",  and  {  of  the 
whole  section  of  chord  plates  would  be  available  for 
tension;  since  an  oblique  section  through  two  holes, 
would  quite  equal  a  direct  transverse  section  through 
one  hole. 

The  amount  of  rivet  section  above  given  is  estimated 
upon  the  assumption  that  each  rivet  must  be  sheared 


ARCH  TRUSS  BRIDGES.  197 

off  in  two  places;  and  that  it  will  resist,  those  shear 
ings,  each,  with  about  f  of  the  force  required  to  pull 
the  rivet  asunder  by  direct  longitudinal  strain. 

It  is  obvious  that  the  two  rivets  e  and/,  Fig.  34 J,  sus 
taining  a  portion  of  the  stress  of  the  chord  plate,  relieve 
in  the  same  degree  the  stress  upon  the  portion  between 
those  rivets  and  the  joint,  or  end  of  the  plate  ;  whence 
it  is  not  necessary  to  preserve  the  same  section  in  the 
portion  thus  relieved,  as  in  other  portions  of  the  plate. 
Therefore  the  rivets  a  and  c,  nearer  to  the  joint,  may 
be  larger  than  e  and/,  when  the  section  of  plates  re 
quires  more  rivet  section  ;  provided  always,  that  the 
least  net  section  of  splice  plates,  have  as  great  an  area 
as  the  chord  plate  has  through  only  one  of  the  smallest 
rivets.  For  instance,  four  f"  rivets  are  sufficient  for 
plates  6"  x  J".  But  plates  6"  xf"  require  more 
rivet  section  — say  £"  for  e  and  /,  and  -|"  for  a  and  c  ; 
while,  the  same  for  the  former  and  V  rivets  for  the  lat 
ter,  give  about  the  required  section  for  plates  6"  x  f". 
This  leaves  in  each  case,  the  same  proportion  of  net 
available  section  of  plates. 

Moreover,  if  rivets  a  and  c  be  placed  opposite  to  each 
other,  and /be  removed  to  «,  the  rivets  being  £"  and 
V  respectively.  Then,  the  smaller  rivets  sustaining 
over  J  of  the  stress,  while  the  others  sustain  less  than 
f,  the  latter  may  cut  off  J  of  the  net  section  (which  is, 
in  this  case  f"  less  than  the  whole  width  of  plate),  and 
still  leave  enough  to  sustain  more  than  their  own 
legitimate  share  of  the  stress. 

This  may  be  done  by  one  rivet  or  two,  placed  op 
posite  c ;  and  thus  the  length  of  splice  plates  may  be 
shortened  to  15  J  inches,  instead  of  20  J,  as  represented 
in  the  diagram.  But,  as  in  this  case,  the  long  plate 
has  a  net  width  of  5J"  and  the  splice  plates,  only  4" 


193  BRIDGE  BUILDING. 

the  latter  require  31J  per  C.  more  thickness  than  the 
former,  so  as  to  nearly  or  quite  balance  the  saving  in 
length. 

As  to  the  proportions  of  parts,  in  this  kind  of  work, 
I  would  suggest  that  the  thickness  of  plates  be  from  Jth 
to  y^th  of  their  width,  and  the  diameter  of  rivets,  from 
1  to  1 J  times  the  thickness  of  plates.  If  plates  be  very 
wide  and  thin,  they  may  be  liable  to  be  strained  un 
evenly,  and  if  very  narrow,  an  unnecessary  proportion 
of  section  is  lost  in  rivet  holes. 

FIG.  34*. 


CXYIIL  The  end  connections  of  plate  chords  of  this 
kind,  may  be  effected  by  riveting  on  side  plates  at  the 
ends,  as  seen  at  E,  Fig.  34J,  so  as  to  give  a  thickness 
that  will  allow  about  J  of  the  width  of  plate  to  be  cut 
away  by  a  hole  for  the  connecting  pin  P,  either  round 
or  oblong  with  square  ends  for  adjusting  keys  or 
wedges. 

Or,  the  side  plates  may  be  omitted,  and  two  key 
holes  made  in  the  middle  of  the  plate,  one  for  a  key 
having  a  thickness  equal  to  the  diameter  of  the  smaller 
rivets,  and  far  enough  from  the  end  to  admit  of  another 
hole  nigher  to  the  end,  with  about  2"  between  the  holes. 
This  may,  if  necessary,  have  twice  the  width  of  the  other 
hole,  and  should  leave  at  least  twice  the  width  of  hole, 
between  hole  and  end. 

The  width  of  the  wider  hole, -{-twice  that  of  the  other, 
should  equal  about  half  the  width  of  the  plate ;  and 
the  keys  should  be  driven  to  an  equal  bearing  before 
the  work  be  subjected  to  use. 


ARCH  TRUSS  BRIDGES.  199 

The  connecting  blocks  used  with  this  chord,  sus 
taining  only  the  horizontal  action  of  diagonals,  may  be 
considerably  lighter  than  those  used  with  the  links, 
especially  in  arch  trusses.  In  order  to  transfer  the 
horizontal  action  of  diagonals  to  the  chords,  mortises 
may  be  made  in  the  plates,  as  seen  at  m  Fig.  34^, not 
wider  than,  the  smallest  rivets  used  in  splicing,  to  re 
ceive  tenons  of  wrought  iron  cast  in  the  block. 

As  to  the  merits  of  the  riveted  plate,  as  compared 
with  the  link  chord,  it  may  be  assumed  that  two  splices 
are  sufficient  for  any 'truss  not  exceeding  100'  long,  and 
that  the  weight  of  splicing  plates  and  rivets  will  equal 
4  or  5  feet  extra  length  of  plates,  say  6  per  cent  upon 
a  chord  80'  long.  To  this  we  have  to  add  about  14 
per  cent  for  extra  section  to  compensate  for  rivet  holes, 
making  20  per  cent  of  iron  lost  in  forming  connections. 

Links  require  about  half  -as  much  extra  material,  to 
be  taken  up  in  bends,  lappings,  and  enlargement  of 
section  at  the  ends;  showing  about  10  per  cent  less 
iron  for  the  link,  than  for  the  plate  chord.  This  would 
amount  to  about  400ft>s.  for  two  trusses  of  80',  with 
links  of  1J"  round  iron.  But  this  may  be  nearly  or 
quite  balanced  by  500  or  600ibs.  of  castings,  which 
may  be  saved  in  weight  of  connecting  blocks. 

The  economy  of  material  being  so  nearly  equal  in 
the  two  chords,  their  relative  merits  must  depend 
mostly  upon  the  comparative  cost  of  manufacture,  and 
the  relative  efficiency  of  the  chords  in  use.  It  is  deemed 
far  from  improbable  that  the  riveted  plate  chord  might 
be  found,  on  fair  and  thorough  trial,  to  be  worthy  of 
extensive  use  in  arch  trusses,  in  place  of  the  link  chord. 
The  fact  that  in  the  plate  chord,  the  iron  is  used  in  its 
original  condition,  as  it  comes  from  the  rollers,  is  cer 
tainly  favorable. 


200  BRIDGE  BUILDING. 


BRIDGES  WITH  PARALLEL  CHORDS. 

CXIX.  These  may  be  constructed  with  or  without 
vertical  members,  and  inform,  either  rectangular,  with 
vertical  end  posts,  or  trapezoidal,  having  inclined 
end  members,  or  king  braces,  as  exbibited  in  Figs. 
12,  13,  18  and  19. 

TRAPEZOIDAL  TRUSS  BRIDGE,  WITH  TENSION  DIAGONALS 
AND  COMPRESSION  VERTICALS. 

For  short  spans,  less  than  70  or  80  feet  long,  the 
simple  cancel,  as  in  Fig.  12,  will  generally  be  used, 
with  trusses  too  low  to  admit  of  connection  between 
upper  chords,  except  in  case  of  deck  bridges. 

The  same  plan  of  lower  chords  composed  of  links 
and  cast  iron  connecting,  blocks,  may  be  used,  as 
already  described  for  the  arch  truss.  The  connecting 
blocks  are  shorter,  and  may  be  cast  in  connection  with 
the  upright,  or  the  latter  may  be  in  a  separate  piece. 
In  the  latter  case,  the  block  should  have  a  suitable  seat 
to  receive  the  upright,  and  keep  it  in  place. 

As  the  upper  chord  depends  upon  the  stiffness  of  the 
beam  and  upright  for  lateral  support  to  keep  it  in  line, 
the  upright  should  be  firmly  attached  to  the  beam,  and 
at  right  angles  therewith. 

There  is  no  means  of  estimating  exactly  the  trans 
verse  force  which  the  chord  may  exert  upon  the  up 
right.  But  if  the  ends  of  chord  segments  be  properly 
squared  and  fitted,  the  lateral  tendency  will  be  quite 
small.  It  is  recommended,  that  each  upright  have  a 
transverse  strength  sufficient  to  withstand  a  force  of 
l,000fts.  acting  at  the  upper  chord  ;  that  it  have  a  web 
and  flange  form  of  section,  with  a  width  of  we!)  at  the 


BRIDGES  WITH  PARALLEL  CHORDS. 


201 


FIG.  35. 


connection  with  the  beam,  not  less  than  ^s  of  the  dis 
tance  of  upper  chord  from  the  beam. 

Fig.  35  will  serve  to  illustrate  the  modes  of  connec 
tion  for  most  of  the  members  of  a  bridge  of  the  kind 
under  consideration.  That 
part  of  the  upright  between  a  arid 
6,  is  contracted  in  length.  Other 
wise,  the  parts  are  represented 
in  nearly  correct  proportions. 
At  c,  is  represented  the  connec 
tion  of  the  upright  with  the  end 
of  the  beam,  by  means  of  a 
double  eye  and  bolt,  as  shown  at 
h.  This  receives  the  web  of  the 
beam,  to  which  it  is  secured  by 
the  transverse  bolt,  which  should 
be  long  enough  to  receive  the 

eye  of  a  swajr  rod  under  both  head  and  nut.  The  stem 
of  this  fixture  extends  through  the  upright  at  its  widest 
part  (whence  it  may  taper  in  both  directions),  and  is 
secured  by  a  nut  upon  a  screw  of  about  1J"  in  diame 
ter.  The  beam  should  rest  with  its  lower  flange  upon 
a  small  projection  cast  upon  the  upright,  and  not  hang 
upon  the  connecting  fixture. 

If  so  preferred,  the  sway  rods  may  be  connected  by 
a  screw  and  nut  cast  in  the  end  of  the  connecting 
block,  as  seen  at  d.  This  plan  has  been  used,  but  the 
connection  by  the  bolt  at  c  is  deemed  preferable. 

The  outer  and  inner  flanges  of  the  upright  at  the 
top,  being  increased  to  nearly  an  inch  in  thickness,  ac 
cording  to  size  of  bridge,  and  extending  3  or  4  inches 
above  the  web,  terminate  in  semicircular  concaves  to 
receive  the  pin  connecting  the  diagonals  with  the 
upper  chord.  A  full  view  of  the  flange  at  the  top  of 
26 


202  BRIDGE  BUILDING. 

the  upright,  with  the  pin  resting  in  the  concave,  is 
shown  at  e. 

A  heavy  cross-bar  from  flange  to  flange  at  a,  and 
light  cross-bars  at  intervals  of  16  to  18  inches  from  a 
to  6,  serve  to  support  the  flanges,  and  stiffen  the  piece. 

The  diagonals  are  formed  with  eyes  to  receive  the 
connecting  pin  at  the  upper  end,  and  screws  and  nuts 
to  connect  with  the  block  at  the  lower  chord,  in  the 
same  manner  as  in  the  arch  truss. 

The  main  diagonals,  those  inclining  outward  from 
the  centre  of  the  truss,  should  be  in  pairs,  and  in  size, 
proportioned  to  the  stress  they  are  liable  to,  as  deter 
mined  by  the  process  fully  described  in  sections 
xxxix,  &c. 

The  links  acting  in  conjunction,  horizontally,  with 
the  main  diagonals,  should  go  on  next  the  end  of  the 
connecting  block,  as  that  arrangement  obviouslypro- 
duces  less  stress  upon  the  block. 

The  upper  chord,  usually  formed  of  hollow  cylinders, 
has  openings  in  the  underside  at  the  joints,  for  uprights 
and  diagonals  to  enter,  where  they  connect  by  means 
of  the  transverse  pin  already  mentioned.  The  cylin 
ders  should  have  an  extra  thickness  for  3  or  4  inches 
from  the  ends,  and  a  strong  collar  around  the  opening, 
to  restore  the  loss  of  strength  occasioned  by  the  open 
ing;  and  the  ends  should  be  squared  in  a  lathe,  to 
secure  a  perfect  joint  and  a  straight  chord. 

If  it  be  required  to  give  a  cambre  to  the  truss,  the 
ends  of  cylinders  should  be  slighly  beveled  at  the  ends, 
making  the  under  side  a  trifle  shorter.  This  is  easily 
effected  by  throwing  the  end  opposite  the  one  being 
turned,  out  of  centre  more  or  less,  according  to  the 
cambre  required.  An  8  panel  truss  requires  an  ex- 
centricity  equal  to  ^  of  the  requiredr  ise  in  the  centre 


BRIDGES  WITH  PARALLEL  CHORDS.  203 

of  the  truss.  For  any  even  number  of  panels,  make  a 
series  of  odd  numbers,  1,  3, 5,  &c.,  to  a  number  of  terms 
equal  to  half  the  number  of  panels;  add  the  terms  of 
the  series,  and  divide  the  required  cambre  by  the  sum, 
and  the  quotient  equals  the  required  excentricity  to 
give  the  proper  bevel. 

For  an  odd  number  of  panels,  take  as  many  even 
numbers  2,  4,  6,  &c.,  as  equal  half  the  greatest  even 
number  of  panels;  add  the  terms  and  divide  as  before 
for  the  excentricity.  For  illustration,  for  8  panels,  the 
four  odd  numbers  1  +  3  +  54-7  =  16,  whence  the  excen 
tricity  should  be  Jg  of  the  cambre,  as  above  stated. 
Fora  7  panel  truss  the  three  even  numbers  2+4+ 6  =  12. 
Hence  the  excentricity  should  be  *2  of  the  cambre. 
The  reason  for  this  ruje  will  be  obvious  without  more 
particular  demonstration. 

At  the  obtuse  angles  of  the  truss,  a  hollow  elbow  is 
inserted  (#,  Fig.  35),  reaching  about  10  inches  each 
way  from  the  angular  point,  at  the  centre  of  the  con 
necting  pin,  with  an  opening  in  the  under  side  for  up 
right  and  diagonals  to  enter,  where  they  are  fastened 
by  a  pin  or  bolt,  as  at  the  intermediate  joints ;  the 
cylinders  meeting  the  elbow,  being  shortened  by  as 
much  as  the  elbow  extends  from  the  angle,  either  way. 

The  vertical  member  connecting  with  the  elbow,  is 
exposed  to  tension  only,  sustaining  a  weight  equal  to 
the  gross  panel  load  of  the  truss.  It  may  be  composed 
of  two  wrought  iron  suspension  rods,  united  in  a  single 
eye  at  the  top,  and  diverging  downward  to  a  connection 
with  the  beam  and  connecting  block;  or,  it  may  be  of 
cast  iron,  like  the  intermediates,  with  wrought  iron  eye 
plates,  in  place  of  the  cast  iron  flanges  with  concaves 
as  seen  at  e.  These  should  be  fastened  by  efficient 
means  to  the  cast  iron  part  of  the  upright;  which  lat- 


204  BRIDGE  BUILDING. 

ter  should  have  a  cross-section  nowhere  less  than 
one  square  inch  to  each  2,000ft)3.  of  the  gross  panel 
load.  A  complete  wrought  iron  connection  from  beam 
to  elbow,  however,  is  to  be  preferred. 

The  thickness  of  web  and  flanges  of  the  uprights, 
should  be  from  f  to  J  inch,  and  the  cross-section  of 
upper  chord  cylinders  should  be  about  20  per  0.  greater 
than  that  of  the  portion  of  bottom  chord  forming  the 
opposite  side  of  the  oblique  parallelogram  included  be 
tween  consecutive  main  diagonals  and  included  sections 
of  chords  ;  as  d  e  k  I,  Fig.  12. 

The  upright  should  be  so  formed  as  to  bring  the  cen 
tres  of  upper  and  lower  chords  in  the  same  vertical 
plane. 

Sway  rods  in  this  class  of  bridges,  should  be  about 
y  in  diameter;  with  a  turn  buckle  near  one  end  for  ad 
justment,  and  an  eye  at  each  end,  for  connection  with 
the  bolt  at  c.  The  screw  working  in  the  turn  buckle 
is  cut  upon  the  short  piece,  which  should  be  J"  larger 
in  diameter  than  the  long  piece  which  has  no  screw 
upon  it. 

The  lower  chords,  king  braces,  and  sway  rods  of  the 
endmost  panels,  connect  with  cast  iron  foot  pieces 
upon  the  abutments,  as  represented 
in  Fig.  36.  The  portion  of  lower 
chord  in  the  end  panels,  usually 
consists  of  single  rods,  instead  of 
links,  with  an  oblong  eye  at  one 
end  to  receive  the  connecting  block,  and  a  screw  and 
nut  for  connection  with  the  foot  piece  (Fig.  36),  at  the 
other  end. 

This  plan  of  construction  will  generally  yield  pre 
cedence  to  the  Arch  Truss  plan,  for  short  spans,  except 
for  deck  bridges  upon  rail  roads,  in  which  case  the 


BRIDGES  WITH  PARALLEL  CHORDS.  205 

structure  will  be  secured  laterally,  by  x  ties,  or  sway 
rods  between  beams,  and  between  king  braces  at  the 
ends ;  no  X  bracing  being  required  between  lower 
chords. 

Low  trusses  constructed  in  the  manner  above  de 
scribed,  have  been  used  satisfactorily  for  supporting 
the  outside  of  wide  side  walks ;  answering  the  pur 
poses  of  a  protection  railing  at  the  same  time.  For 
this  purpose,  the  uprights  are  only  5  or  6  feet  long,  so 
as  to  bring  the  upper  chord  about  4  feet  above  the 
flooring.  The  first  instance  of  this  kind  was  in  the 
case  of  the  canal  bridge  on  Genesee  street  in  Utica, 
built  18  or  20  years  ago,  and  repeatedly  copied  since. 

CXX.  Bridges  from  80  to  100  feet  for  common  roads 
may  be  constructed  with  single  canceled  trusses,  13  to  14 
feet  high  ;  in  which  case  the  panels  will  require  to  be 
wide  (horizontally)  in  order  to  avoid  an  inclination  of 
diagonals  too  steep  for  good  economy. 

But  for  railroad  purposes,  the  trusses  require  a  depth 
of  about  20  feet  to  afford  sufficient  head  room  under 
the  top  connections,  unless  the  beams  be  suspended 
below  the  bottom  chords.  Hence,  the 

Double  Cancelated  Truss 

should  be  adopted  for  "  through  bridges "  of  spans 
exceeding  70  or  80  feet. 

Figures  18  and  20  exhibit  in  outline,  the  general 
character  of  the  double  cancelated  trapezoidal  truss 
bridge ;  and,  it  is  only  necessary  in  this  place,  to  de. 
scribe  feasible  modes  of  forming  and  connecting  the 
various  members ;  which  may  be  done  essentially  as 
described  in  the  preceding  section,  with  such  modifi 
cations  as  follow. 


206 


BRIDGE  BUILDING. 


FIG.  37. 


Cast  Iron  Uprights 

are  composed  of  two  or  more  pieces.  When  of  two 
pieces,  they  may  be  connected  by  flanges  and  bolts  at 
the  centre,  where  they  should  have  a  diameter  of  about 
$*ij-  of  the  length,  and  a  cross-section  determined  by 
the  maximum  stress,  and  the  power  of  resistance  of 
the  material,  as  indicated  in  the  table  [XGIII.] 

The  upright  may  taper  from  the  centre  to  either  end 
to  a  diameter  of  5  to  6  inches,  internally.     The  lower 

end  is  to  stand  upon 
a  properly  formed 
seat  (h  Fig.  37), 
upon  the  connect 
ing  block  of  the 
lower  chord,  and 
may  have  an  open 
ing  at  the  bottom, 
upon  the  inner  side, 
where  the  beam 
may  enter  and  rest 
upon  a  seat  (e),  inside  of  the  upright,  upon  the  con 
necting  block.  The  strength  destroyed  by  this  cutting 
the  post  should  be  restored  by  additional  metal  in  a 
band  or  collar  (c,  Fig.  37),  around  the  opening,  and, 
if  necessary,  by  the  wing  flanges  dd,  extending  6  or  8 
inches  above  the  opening.  To  avoid  too  much  cutting 
of  the  post,  the  flanges  of  the  beams  may  be  reduced 
to  3  or  3J  inches  in  width.  The  post  and  beam  seat 
upon  the  connecting  block  may  be  elevated  3  or  4 
inches  above  the  links,  as  may  be  required,  so  as  to 
allow  sway  rods  to  pass  through  with  simple  screws 
and  nuts  for  adjustment;  thus  dispensing  with  turn- 
buckles. 


BRIDGES  WITH  PARALLEL  CHORDS.  207 

Holes  should  be  cast  in  the  central  part  of  the  post, 
for  diagonals  to  pass  obliquely  through.  Or,  what  is 
perhaps  better,  the  connecting  bolts  may  be  length 
ened  so  as  to  permit  the  insertion  of  an  open  box,  or 
frame,  between  the  flanges,  as  seen  at  a,  Fig.  37. 
This  intermediate  piece  should  be  so  constructed  as 
to  close  the  ends  of  the  hollow  pieces  meeting  it,  and 
prevent  the  water  from  getting  inside. 

The  top  end  of  the  upright  is  forked,  with  concaves 
for  the  connecting  pin  to  rest  in,  as  described  in  the 
last  section,  and  as  seen  at  a,  Fig.  38.  The  cap  piece 
of  the  post  may  be  cast  separate,  or  in  connection  with 
the  upper  half  of  the  column.  Both  plans  have  been 
satisfactorily  used.  All  joints,  when  practicable, 
should  be  accurately  fitted  by  turning  or  planing. 

This  plan  of  a  cast  iron  upright,  composed  of  two 
principal  parts,  with  or  without  the  centre  piece,  is 
perhaps  as  good  as  any  for  general  use ;  the  principal 
disadvantage  being  the  difficulty  of  giving  a  sufficient 
diameter  in  the  middle  for  stiffness,  without  two  much 
reducing  the  thickness  of  metal,  or  increasing  the 
amount  of  cross-section  beyond  the  proper  theoretical 
proportions. 

To  obviate  this  difficulty,  the  device  adopted  in  the 
original  model  of  the  Trapezoidal  bridge,  was  that  of 
using  truss-rods,  or  stiffening  rods,  to  secure  the  post 
against  lateral  deflection,  after  the  mannner  shown  in 
Fig.  38. 

In  the  case  of  using  stiffening  rods  for  the  uprights, 
it  may  be  recommended  to  form  each  half  of  the  column 
in  two  pieces,  somewhat  in  the  manner  above  described 
for  the  whole  one,  without  stiffeners;  making  the 
piece  forming  the  end  portion  about  Jth  shorter 


208 


BRIDGE  BUILDING. 


than  the  other,  with  a  strong  flange  at  the  larger  end, 
to  afford  attachments  for  the  stiffening  rods. 


Fm.  38. 


In  Fig.  38,  a  c  d  exhibits  the  upper  half  of  the  up 
right  ;  A,  the  stretcher  at  d  ;  /,-,  the  flange  at  c  (enlarged), 
and  £,  j,  enlarged  sections  of  the  two  ends  forming  the 
joint  at  c.  The  piece  running  toward  the  centre  has  no 
flange  at  <?,  but  has  :m  increase  of  thickness  for  a  short 
distance  from  the  joint,  as  shown  atj,  and  a  diameter 
about  I"  larger  than  the  abutting  piece,  which  latter 
has  a  small  burr  entering  the  former  J"  or  J"  to  keep 
the  ends  in  place.  At  tf,  each  of  the  pieces  meeting 
at  that  point,  has  a  bi-furcation,  so  as  to  form  an  open 
ing  for  diagonals  to  pass  through,  at  the  same  time 
passing  through  the  stretcher  h. 

The  lower  half  of  the  upright  is  the  same  as  the 
upper,  except  the  end,  which  is  squared  to  fit  a  flat 
bearing  upon  the  connecting  block.  An  enlarged  ver 
tical  section  of  the  lower  end  is  shown  at  £,  Fig.  38. 
See  also  Fig.  37,  where  is  shown  the  arrangement  for 
the  beam  to  enter  the  opening  in  the  lower  part  of  the 
upright,  as  described  a  few  pages  back. 

Floor  beams  of  wood  or  iron  may  be  suspended  be 
low  the  chords  by  bolts  passing  down  through  the 
connecting  blocks,  or,  wooden  beams  may  be  in  two 


BRIDGES  WITH  PARALLEL  CHORDS.  209 

parts,  resting  upon  flanges  cast  upon  the  upright  a^out 
3"  above  the  lower  end  ;  the  beam  timbers  being  hol 
lowed  out  upon  the  insides,  so  as  to  embrace  the  up 
right,  in  part,  leaving  a  space  of  2  or  3  inches  between, 
and  secured  in  place  by  bolts  and  separating  blocks. 

The  mode  of  inserting  iron  beams  by  means  of  open 
ings  in  the  uprights,  has  already  been  explained. 
Lateral  x  ties,  or  sway-rods  may  be  inserted  by  bolting 
to  the  beams  (Figs.  31  and  33),  attaching  to  the  inner 
end  of  connecting  blocks,  as  at  </,  Fig.  35,  or  by  passing 
through  the  block  between  the  links  and  the  post  and 
beam  seat,  in  the  manner  referred  to  two  pages  back. 

Diagonal  tics  of  wrought  iron,  and  transverse  struts 

O  O  «     ' 

of  wrought  or  cast  iron,  are  also  required  between  the 
upper  chords,  to  keep  them  in  line.  Cast  iron  cross- 
struts  may  have  the  web  and  flange  form  of  section, 
with  shallow  sockets  at  the  ends,  to  admit  the  connect 
ing  bolts  at  the  upper  chord  to  enter,  after  passing 
through  eyes  upon  the  upper  sway-rods  and  nuts  to 
hold  them  in  place.  These  sway -rods  require  turn- 
buckles  for  adjustment,  when  they  extend  across  one 
panel  only.  Bat  if  the  bridge  be  wide  between  trusses, 
the  rod  may  extend  only  from  the  end  of  one  cross- 
strut  to  the  centre  of  the  next,  where  it  may  pass 
through  the  strut,  and  receive  a  nut  on  the  end.  Thus, 
four  rods  meeting  at  the  centre  of  the  strut,  each 
having  its  appropriate  hole  to  pass  through,  all  as  near 
to  one  another  as  practicable,  with  sufficient  space  for 
nuts  to  turn  (see  a  and  e,  Fig.  39),  it  forms  a  conven 
ient  arrangement  for  adjusting  the  rods  to  a  proper 
tension,  at  the  same  time  affording  lateral  steadiness  to 
the  cross -strut. 

The  end-most  struts,  however,  should  have  no  rods 
connecting  with  them  in  the  centre,  as  they  can  have 


210 


BRIDGE  BUILDING. 


no  antagonist  rods  on  the  opposite  sides  to  prevent  the 
springing  of  the  struts.  The  end  panels  should  have 
two.  full  diagonals  with  turn-buckles,  and  two  half 
diagonals  connecting  with  the  centre  of  next  strut. 


FIG. 


In  Fig.  39,  a  shows  the  middle  of  the  cross-strut, 
with  the  upper  flange  removed  ;  c,  a  joint  of  the  upper 
chord,  where  the  connecting  bolt  passes  transversely, 
receiving  eyes  of  sway-rods,  and  nut,  and  entering  the 
end  of  the  strut  at  d\  the  upper  part  of  the  strut  being 
removed,  down  to  the  socket.  The  bolt  bears  upon  a 
slight  swell  in  the  bottom  of  the  socket,  to  ensure  a 
central  thrust :  (see  also,  6,  Fig.  38).  At  e  is  presented 
a  side  view  of  the  centre  of  the  strut,  showing  the  ar 
rangement  of  the  holes. 

A  similar  device  has  been  used  with  good  effect  for 
giving  lateral  support  to  posts  or  thrust  uprights,  of 
the  web  and  flange  form,  so  proportioned  as  to  have 
greater  stiffness  transversely  than  lengthwise  of  the 
truss. 

It  has  been  demonstrated  that  the  weight  sustained 
by  these  posts,  increases  toward  the  ends  of  the  truss, 
while  the  tension  of  counter  diagonals  runs  out  to 
nothing,  a  little  way  from  the  centre  of  the  truss.  For 
instance,  4/6  Fig.  18,  sustains  §w" — Ifw',  which  is  a 
negative  quantity  whenever  w  is  less  than  4w/,  that  is, 


BRIDGES  WITH  PARALLEL  CHORDS.  211 

when  the  greatest  movable  load  is  less  than  four  times 
the  weight  of  structure,  as  is  usually  the  case.  But 
instead  of  dispensing  with  that  member,  and  other 
counters  on  the  left,  they  may  be  made  in  two  pieces 
each,  off"  or  £"  iron,  connecting  with  the  upright  at 
the  crossing  by  screws  and  nuts,  in  the  manner  above 
described ;  thus  preventing  the  uprights  from  deflect 
ing  lengthwise  of  the  truss,  where  the  greatest  weights 
act  upon  them,  and  where  otherwise,  they  would  re 
quire  to  be  heavier. 

GENERAL  TRANSVERSE  SUPPORT. 

CXXI.  The  system  of  cross-struts  and  diagonal  ties 
serves  to  preserve  the  upper  chords  in  line,  but  does 
not  prevent  the  whole  structure  from  swaying  bodily 
to  the  right  or  left ;  a  result  which  would  be  fatal  to 
the  structure. 

In  the  arch  truss  Fig.  27,  the  width  of  base  at  tlie 
bearings  upon  abutments,  resulting  from  the  peculiar 
form  of  the  arch,  affords  the  required  stability  in  this 
respect. 

In  case  of  the  trapezoidal  truss,  when  high,  various 
devices  have  been  resorted  to  for  producing  the 
same  results.  For  deck  bridges,  cross  tying  between 
king  braces  at  the  ends,  is  an  easy  and  efficient  means 
of  accomplishing  the  object.  For  through  bridges, 
guys  from  the  connecting  bolt  at  the  elbow  of  the  ob 
tuse  angle,  anchored  in  the  abutment,  may  be  em- 
ploj^ed.  But  this  requires  extra  length  of  abutments 
and  piers,  and  the  effects  of  change  of  temperature, 
are,  to  tighten  and  slacken  the  guys,  so  as  to  impair 
their  efficiency. 

To  obviate  the  latter  objection,  double  acting  guys 
(acting  by  thrust  and  tension),  applied  at  one  side  only 


212  BRIDGE  BUILDING. 

of  the  bridge,  have  been  employed ;  the  effect  of 
temperature  being  only  to  very  slightly  sway  the 
bridge  laterally,  but  not  so  as  to  be  detrimental  to  sta 
bility.  This  also,  requires  5  or  6  feet  more  length  of 
pier,  than  what  is  necessary  to  bear  the  vertical  pres 
sure. 

Again,  the  king  braces  have  been  made  with  two 
branches  diverging  from  the  elbow  to  a  base  of  2  or  3 
feet  in  width,  according  to  height  of  truss.  This  plan 
has  been  used  in  a  large  number  of  bridges,  with  sa 
tisfactory  results.  But  it  contracts  to  a  small  degree, 
the  available  width  of  bridge ;  not,  however,  so  as  to 
produce  material  inconvenience. 

Another  device  is,  the  introduction  of  two  or  more 
long  beams,  extending  5  or  6  feet  outside  of  the  trusses, 
say  at  the  first  thrust  uprights  from  the  ends  (as  over 
Figs.  3J,  3J,  Fig.  18),  with  guys  extending  from  the 
connecting  bolt  at  the  upper  chord,  to  the  ends  of  said 
long  beams  (see  g  Fig.  38). 

Arches  may  also  be  introduced  at  the  ends  of  the 
bridge,  attached  to  the  king  braces,  say  a  quarter  of 
the  way  down  from  the  top,  and  with  the  connectingbolt 
at  the  elbow.  These  may  be  made  with  a  full,  or  an 
open-work  web,  and  flanges  of  2J  or  2J  inch  angle 
iron  upon  both  sides  of  the  web,  at  the  top,  and  around 
the  arch,  and  either  angle  iron  or  plain  flat  bars,  along 
the  sides  next  the  king  braces. 

A  web  of  jV  plates  placed  edge  to  edge,  and  bat 
tened  upon  both  sides  with  plates  of  the  same  about 
4/r  wide,  riveted  alternately  on  each  side  of  the  seam, 
with  angle  iron,  etc.,  as  above,  riveted  once  in  6",  forms 
a  stiff  and  substantial  arch  for  the  purpose  under  con 
sideration,  such  as  have  been  used  effectively  in  a 
bridge  of  160ft.  span. 


BRIDGES  WITH  PARALLEL  CHORDS. 


213 


Moreover,  simple  arch  braces  extending  from  the 
king  brace  to  a  stiff  and  substantial  cross  beam  from 

elbow  to  elbow 
(see  Fig.  40),  will 
effect  nearly  the 
same  result  as  the 
arch.  In  both 
cases,  a  considera 
ble  degree  of  lateral 
stress  is  liable  to 
be  thrown  upon  the 
king  braces,  which 
accordingly  should 
be  strong,  or  sup 
ported  by  truss 
rods,  and  struts 
opposite  the  feet  of  the  arch  or  braces. 

Whether  the  truss  rods  be  used  or  not,  it  is  advisa 
ble  that  the  connection  with  the  king  brace  be  made 
by  means  of  a  bolt  running  through  the  whole  dia 
meter  of  the  king  brace,  with  nut  or  shoulder  bearing 
externally  and  internally  upon  both  sides,  to  counteract 
any  tendency  to  collapse. 

Fig.  40  presents  an  end  view  of  a  bridge,  showing 
arch  braces,  with  truss  rods  to  sustain  the  thrust  of 
arch  braces  against  king  braces.  The  internal  figure 
gives  an  enlarged  view  of  the  connection  at  the  elbow. 
A  strap  a  (about  }"x5"),  bent  twice  at  right  angles, 
is  riveted  or  bolted  to  the  flanges  of  an  I  beam 
(about  9"  deep),  leaving  a  space  of  about  4  inches  from 
the  end  of  the  I  beam,  for  eyes  of  two  sway  rods  and  a 
nut  upon  the  large  connecting  bolt.  This  bolt  in  large 
bridges  being  from  3  to  4  inches  in  diameter  through 
the  elbow,  is  reduced  to  2  or  2J  inches  in  the  part  pro- 


214  BRIDGE  BUILDING. 

jecting  through  the  strap  above  mentioned,  and  the 
eyes  of  sway  rods. 

The  truss  rods  may  not  be  necessary  (with  substan 
tial  king  braces),  for  spans  not  exceeding  150  feet, 
But  they  will  add  to  the  security,  in  all  cases  of  rail 
road  bridges  having  cast  iron  king  braces.  These 
members  being  over  twice  the  length  of  the  cylinders 
in  the  upper  chord,  are  usually  cast  in  two  pieces,  and 
connected  by  bolts  and  flanges  in  the  middle,  where 
they  have  a  diameter  of  about  2^  of  the  length  of 
brace,  and  taper  to  the  size  of  the  upper  chord  at  the 
ends. 

CXXII.  WROUGHT  IRON  THRUST  MEMBERS. 

The  trapezoidal  bridge,  as  described  in  detail  in  the 
preceding  section,  and  as  originally  intended,  is  a 
wrought  and  cast  iron  bridge.  But  it  will  readily  be 
seen  that  with  slight  modification  of  detail,  it  is  easily 
adapted  to  the  use  of  wrought  iron  upper  chord,  verti 
cal  posts,  and  main  end  braces ;  which  latter,  for  con 
venience,  have  been  designated  in  this  work,  as  king 
braces. 

All  of  these  members  may  be  in  the  form  of  the 
patent  wrought  iron  column  of  the  Phoenix  Iron  Co. 
of  Pennsylvania,  formed  of  flanged  segments,  united 
by  riveting ;  or  of  rectangular  wrought  iron  trunks,  as 
well  as  various  other  forms  of  section. 

For  the  Phoenix  column,  a  cast  iron  connecting 
piece  may  be  inserted  at  the  joints  of  the  upper  chord, 
with  ends  formed  to  enter  the  squared  ends  of  the 
chord  cylinders,  and  receive  them  against  a  shoulder 
of  the  connecting  piece.  This  piece  may  have  an 
opening  in  the  under  side  to  receive  the  diagonals 
and  uprights,  where  they  are  secured  by  a  transverse 


WROUGHT  IRON  THRUST  MEMBERS. 


215 


connecting  bolt,  in  the  same  manner  as  at  the  joint  of 
the  cast  iron  chord  cylinders,  as  before  described.  In. 
this  case  the  upright  may  have  a  cast  iron  top  piece, 
formed  as  seen  in  Figs.  35  and  38  upon  the  top  of  cast 
iron  uprights.  A  separate  top  piece  has  sometimes 
been  used  with  cast  iron  verticals. 

FIG.  41. 


The  connecting  piece  may  also  be  formed  as  indi 
cated  in  Fig.  41,  with  a  downward  branch  like  pro 
cess  to  meet  and  receive  the  squared  end  of  the  vertical 
in  the  same  manner  as  the  horizontal  part  connects 
with  chord  cylinders.  In  this  case  the  connecting 
piece  must  have  openings  as  at  b  b  Fig.  41,  for  the  eyes 
diagonals  to  enter. 

Fig.  41,  shows  an  inside  view  of  the  joint  piecej  as 
it  would  appear  if  cut  vertically  and  longitudinally, 
and  the  near  half  removed.  The  horizontal  part  con 
sists  of  a  cylindrical  shell  a  little  thicker  than  the 
wrought  iron  chord  cylinder,  with  ribs  upon  the  out 
side  corresponding  with  those  of  the  wrought  cylinders, 
and  as  shown  in  end  view  c.  Upon  the  inside,  the 
ring  and  flanges  a  a,  project  inward,  leaving  usually  a 
space  of  about  5  inches  (according  to  dimensions  of 


216  BRIDGE  BUILDING. 

bridge),  for  eyes  of  diagonals.     These  are  to  ease  the 
lateral  strain  of  the  connecting  bolt  or  pin. 

The  process  meeting  the  vertical,  may  be  rectangu 
lar  in  horizontal  section,  composed  of  two  parallel  flat 
plates,  in  form  as  may  suit  the  taste  of  the  designer, 
united  by  two  irregular  plates  formed  to  the  profile  of 
the  parallel  plates.  The  openings  for  diagonals,  are,  of 
course,  through  the  irregular  plates.  These  are  drawn 
in  at  the  bottom  so  as  to  form  a  square  with  the  paral 
lel  sides,  large  enough  to  cover  the  flanges  of  fhe  4 
segment  column  selected  for  the  upright.  See  Fig.  41. 

The  inside  of  the  square  d,  is  filled  in  to  form  a  hol 
low  round,  about  an  inch  less  in  diameter  than  the 
hollow  of  the  column,  that  it  may  have  a  ring  or  collar 
(represented  by  the  inner  white  ring  around  d),  project 
ing  about  2  inches  beyond  the  shoulder  into  the  wrought 
iron  column. 

On  the  top  of  the  joint  piece  may  be  an  arrangement 
of  oblique  holes  for  the  attachment  of  lateral  X  ties, 
and  on  the  inside,  facing  the  opposite  truss,  an  abutting 
seat  for  the  cross-strut,  which  may  be  in  the  form  of  a 
6"  I  beam,  or  such  other  form  as  may  be  preferred. 

The  foot  of  the  post  may  stand  upon  a  properly 
formed  seat  upon  the  connecting  block  of  the  lower 
chord,  with  an  opening  to  receive  the  beam,  in  the 
same  manner  as  described  for  the  cast  iron  post.  See 
Fig.  37. 

It  will  be  necessary  ror  diagonals  to  pass  through  the 
centres  of  uprights,  and  for  that  purpose  10  or  12  inches 
in  length,  as  may  be  necessary,  may  be  left  out  of  two 
opposite  segments,  and  the  strength  thus  lost,  restored 
by  additional  metal,  in  such  form  as  may  be  found  con 
venient  and  efficient.  Or,  a  cast-iron  middle  piece  may 
be  inserted  in  the  upright. 


WROUGHT  IRON  THRUST  MEMBERS.  217 

lu  the  case  of  an  upper  chord  of  rectangular  trunks, 
and  uprights  of  other  than  a  cylindrical  form,  the  joint 
piece  will  be  correspondingly  modified. 

The  position  of  diagonals  may  be  reversed,  connect 
ing  by  an  eye  with  a  wrought  cylindrical  connecting 
pin  at  the  lower  chord,  and  by  screw  and  nut  with  the 
joint  piece  of  the  upper  chord.  This  involves  merely 
a  question  of  practical  economy  and  convenience. 

Sometimes,  also,  the  connection  is  made  by  an  eye 
at  both  ends  of  the  diagonal,  depending  upon  accuracy, 
as  to  length,  in  the  manufacture,  for  the  proper  ad 
justment  of  parts.  It  is  also  practicable  to  provide 
means  of  adjustment  in  the  length  of  vertical  members. 

CXXIII.  But,  to  enumerate  all  the  changes,  and 
peculiarities  of  detail  admissible  in  the  construction  of 
the  Trapezoidal  Truss  Bridge,  even  if  practicable,  could 
hardly  be  regarded  as  expedient  in  this  place.  The 
essential  requisities  are,  to  provide  material  enough  of 
good  quality  in  all  parts,  to  withstand  the  forces  to  which 
they  are  respectively  liable,  with  efficient  connections 
of  parts,  by  the  most  direct  and  simple  means,  and  with 
s'ich  an  arrangement  and  adjustment  as  may  produce 
the  most  uniform  degree  of  strain  upon  all  parts  of 
each  member.  For  instance,  ecah  section  of  the  lower 
chord  is  usually  composed  of  several  bars,  and  it  is  im 
portant  that  each  should  sustain  its  proportionate  share 
of  the  stress. 

In  the  link  chord  composed  of  two  links  to  each 
panel,  if  the  links  be  properly  fitted,  the  two  sides  of 
each  must  act  very  nearly  alike,  while  the  connecting 
block  acts  as  a  sort  of  balance  beam  to  equalize  the 
tension  of  links  acting  upon  its  two  ends  ;  and,  if  the 
two  links  of  a  pair  vary  slightly  in  length,  the  connect- 

28 


....... 

•»?%«• 


218  BRIDGE  BUILDING. 

ing  block  still  secures  equality  of  stress  upon  the  two. 
The  same  is  the  case  with  regard  to  a  chord  composed 
of  two  eye  bars  instead  of  links,  to  each  panel. 

But  the  serious  mistake  is  .sometimes  committed,  of 
putting  the  two  links  or  bars  upon  the  same  side  of 

those  in  the  succeeding  panel, 
FlG-  42-  as  in  Fig  42  ;  where  it  is  ob- 

F vious  that  the  inside  links  (a, 

*   by  c),  are  exposed  to  more  ac 
tion  than  d,  e,f. 

For,  if  the  inside  links  be 
8",  and  the  outside  ones  4"  from  centre  of  pin,  since 
a  and  b  tend  to  turn  the  pin  in  one  direction  about  its 
centre,  and  d  and  e  in  the  opposite  direction,  the  forces 
being  in  equilebirio  —  the  moments  (with  respect  to  the 
centre),  of  forces  tending  in  one  direction,  must  be 
equal  to  those  of  forces  tending  in  the  opposite  direc 
tion.  Hence,  representing  the  stresses  of  the  several 
links  by  the  letters  designating  them  respectively  on 
the  diagram,  we  have  3  X  (a  -f  b)  =  4  x  (d  -f  e),  whence, 
a  +  b  =  |  (d  -f  e) ;  showing  J  more  stress  upon  the  in 
side  than  upon  the  outside  links. 

On  the  contrary,  if  the  link  e,  be  removed  to  e'  upon 
the  inside  of  a,  then  d  and  e'  act  in  one  direction,  and 
a  and  b  in  the  otjier;  and,  assuming  as  before,  the 
inside  links  to  be  3",  and  the  outside  ones  4"  from 
centre  of  pin,  we  have  4a  -f  36  =  4d  +  3e'.  But  a  -f  d 
=  b  +  e',  and  if  the  force  be  communicated  at  the  ends, 
equally  upon  the  two , sides  of  the  chord,  giving  equal 
stress  upon  a  and  o?,  for  instance,  the  tendency  is  to  an 
even  balanced  action  throughout  the  length  of  chord. 

Hence  the  two  links  of  each  panel  should  always 
act  upon  the  connecting  block  or  pin,  at  equal  dis 
tances  from  centre  of  pin. 


MULTIPLEX  CHORDS. 


219 


MULTIPLEX  CHORDS. 

CXXIV.  In  very  long  or  heavy  bridges,  the  required 
amount  of  chord  section  in  the  middle  portion  of  the 
truss,  is  so  great,  that  k  is  deemed  expedient  to  intro 
duce  more  than  two  links  or  eye  hars  to  the  panel. 
This  is  sometimes  done  by  alternating  them  upon  the 
connecting  pin,  increasing  the  number  and  sizes  ac 
cording  to  the  increase  of  stress  from  panel  to  panel 
toward  the  centre. 

This  mode  of  construction,  unless  the  bars  be  ar 
ranged  and  proportioned  with  almost  impracticable 
care  and  nicety,  is  liable  to  be  attended  by  an  accumu 
lation  of  lateral  strain  upon  the  connecting  pin,  beyond 
what  it  can  bear  without  bending,  or  springing  so  much 
as  to  materially  disturb  the  equality  of  stress  upon 
the  links,  or  chord  bars. 

FIG.  43. 


To  illustrate  this  subject,  let  Fig.  43,  represent  one 
quarter  of  the  chord  of  a  16  panel  bridge.  The  line 
CC  may  denote  the  central  axis  of  the  chord  running 
through  the  centres  of  connecting  pins ;  D,  at  a  dis 
tance  of,  say  8"  from  C,  the  line  in  which  the  diago 
nals  act  upon  pins,  and  the  other  parallel  lines  at 
intervals  of  3"  from  D,  and  from  one  another  (see  Figs. 


220  BRIDGE  BUILDING. 

on  right  hand  of  diagram),  the  centres  of  thickness  of 
links,  at  which  points  the  action  of  respective  links 
is  supposed  to  be  concentrated  upon  the  pins.  Also, 
let  a,  by  c,  etc.,  represent  the  panels  of  the  chords. 

Now,  if  15W,  or  15,  represent  the  stress  upon  the 
chord  in  the  two  first  panels,  a  and  6,  that  of  the  suc 
ceeding  panels  to  the  centre,  will  be  as  22,  34,  44,  52, 
58  and  62  (see  lower  figures  in  diagram),  and  the  dia 
gonals  (producing  increments  of  action  upon  chord), 
will  have  a  horizontal  action  represented  by  7  in  panel 
b,  by  12  in  panel  c,  and  so  on  by  10,  8,  6,  4.  These 
being  added  successively  to  15,  produce  the  numbers 
just  stated  for  the  chord  in  the  several  panels. 

The  first  three  panels,  a,b  and  c,  require  only  one  link 
upon  each  side,  as  indicated  by  the  oblique  black  lines. 
The  4th  panel,  d,  may  have  2  links  on  a  side,  and  the 
most  favorable  position  for  them,  as  regards  action 
upon  connecting  pins,  will  be  as  shown,  diverging 
from  the  central  axis,  so  as  to  bring  the  end  toward 
the  abutment,  nearest  to  the  main  diagonal  connecting 
with  the  same  pin. 

The  first  pin,  connecting  a  and  6,  having  two  equal 
forces  acting  in  opposition,  but  at  different  distances 
from  the  centre  line  (7,  we  take  the  moments  of  these 
forces  with  respect  to  that  line ,  which  are,  for  a, 
15xl4=210,andfor6, 15x11=165.  The  difference  (45) 
between  these  moments,  equals  the  moment  of  the 
resultant,  or  the  lateral  stress  of  the  pin,  exerted  on  a 
leverage  of  1". 

Assuming  the  value  of  W,  our  unit  of  stress  (and 
always  understood  as  annexed  to  the  figures  denoting 
stress),  to  represent  5,000ft>s.  we  have  for  stress  of  pin 
in  this  case,  45  X  5,000-*-L.  The  L,  being  V  may  be 
omitted  in  the  expression. 


MULTIPLEX  CHORDS.  £21 

Then,rnakingz=diameterofpin,itsresistingpower= 
A5.x4,500  (see  [xcvm])=  .785z2  x  x  x  4,500  -r-  1"= 
3,532. 5r3;  and  putting  this  equal  to  45x5,000  (the  stress 
above  found),  we  obtain  £=4"  (very  n  early), = required 
diameter  of  pin. 

At  the  next  pin  we  take  the  moments  of  one  link 
15xl4"=210,  and  one  diagonal,  7  x8"=56,  making  266 
in  one  direction,  against  that  of  one  link,  22x11"= 
242.  Hence  the  resultant  moment  =  24,  and  24  X 
5,000=3,532.5x3,  gives  the  required  diameter  of  pin  in 
the  centre,  £==3J',  nearly.  But  this  is  the  general 
stress  in  the  portion  of  pin  between  diagonals,  and 
may  be  greater  or  less  than  at  certain  points  where 
forces  are  applied.  For  instance,  if  the  aggregate 
moments  of  forces  in  opposite  directions  be  equal,  the 
resultant  moment  is  nothing,  and  the  middle  portion 
of  the  pin,  between  diagonals  has  no  stress,  and  might 
be  cut  out  and  removed,  as  far  as  strength  of  chord  is 
concerned.  In  the  case  in  hand,  the  moment  of  link 
6,  with  respect  to  link  c,  equals  15"x3=  45=stress  of 
pin  at  centre  of  c.  Hence  the  required  diameter  at 
this  point  is  found  by  the  equation  45x5,000=3,532.5 
Xx3,  whence  £=4",  the  same  as  pin  ]STo.  1. 

At  the  next  pin,  if  we  add  another  link,  making  2 
links  sustaining  34W,  at  an  average  of  14"  from  centre, 
giving  a  moment  of  476,  against  one  link,  22x14,  + 
one  diagonal  12x8=404,  we  obtain  a  resultant  mo 
ment  of  72  ;  whence,  72x5,000  =  3,532.5x3,  and  x  = 
4.67  inches,  =  required  central  diameter  of  pin,  and  as 
will  be  readily  seen  on  trial,  the  greatest  required  at 
any  point. 

Again,  assuming  at  the  4th  pin  2  links  and  1  dia 
gonal  against  two  links,  we  have  for  the  former, 
34x17" +  10x8  =  658,  and  for  the  latter,  44x14  = 


222  BRIDGE  BUILDING. 

616,  whence  the  resultant  moment  is  42.  Therefore 
the  equation  42x5,000  =  3,532.5z3,  gives;r  =  3.9  inches, 
=  required  diameter  in  centre,  while  for  the  outside 
link  on  this  pin,  the  stress,  17,  multiplied  by  3  shows 


a  moment  of  51.  Hence,  x  =  ^*0     =  4.16  inches 

O,Oo/a.O 

=  required  diameter  at  that  point. 

At  the  5th  pin,  there  are  3  links,  against  2  links  and 
one  diagonal,  giving  moments  for  the  latter,  44x17  + 
8x8  =  812,  and  for  the  former,  52x17  =  884  ;  whence 
the  resultant  moment  =  72,  and  x  =  &  (?2xj;-"uo)  =  4.67 

,  #,532.5 

inches. 

The  moments  at  pin  No.  6,  are,  for  3  links,  52x20,  -f 
(for  diagonal)  6x8  ==1088,  in  one  direction,  and  for  3 
links,  58x17  =  986,  giving  a  resultant  of  102  ;  whence, 


Lastly,  adding  another  link  at  the  7th  pin,  the 
moments  are  58x20  -f  (for  diagonal)  4x8,  =  1,192,' 
against  62x20''  =  1240,  whence  the  resultant  is  48, 
and*  -X^jgp-  4-08. 

In  this  case  the  eyes,  or  link-ends  are  supposed  to  be 
bored  in  the  direction  of  the  pin,  a  little  obliquely  to 
the  direction  of  the  link,  so  as  to  bear  through  the 
whole  thickness,  as  long  as  the  pins  remain  perfectly 
straight.  But  the  pins  having  a  degree  of  elasticity, 
and  considerable  length,  must  yield  to  the  action  of 
links,  springing  more  or  less  in  the  direction  of  the 
greater  sum  of  moments.  It  will  be  seen,  moreover, 
that  in  each  case,  the  consecutive  ends  entering  the 
outside  link,  as  3  and  4,  5  and  6,  &c.,  are  always  sprung 
toward  one  another  ;  the  inevitable  result  of  which 
must  be,  a  relief  or  relaxation  of  the  outside  link, 
whence  it  must  sustain  a  less  degree  of  strain  than  its 
fellows  located  farther  from  the  ends  of  the  pins. 


MULTIPLEX  CHORDS.  223 

* 

Now,  as  a  12  foot  link,  under  a  stress  of  10,000ft>s.  to 
the  inch  is  extended  less  than  — f— -  of  a  foot,  a  slight 

1  jUUU 

springing  of  connecting  pins  would  relax  the  outside 
links  materially,  especially  when  the  pins  tend  to  spring 
toward  one  another. 

Again,  if  the  links  run  parallel  with  the  centre  of 
chord,  and  at  right  angles  with  the  connecting  pins, 
as  indicated  by  the  double  black  lines  (Fig.  43),  the 
moments  of  forces  upon  — pin  No.  5,  for  instance,  will 
be  —  for  3  links  acting  toward  .the  right  hand,  44  x 
17  -f  (for  diagonal)  8x8  =  812,  against  3  links  acting 
toward  the  left,  with  moments  equal  to  52  x20  =  1,040, 

showing  a  difference  of  228  ;  whence£=^(228*5>000)  = 

3,582  5 

6.85  inches  -=  required  diameter  of  pin  at  the  centre. 

At  pin  No.  6,  are  3  links  with  a  combined  moment 
of  52  x  20,  -f  (for  diagonal),  6x8,  =  1076,  against  3 
links  with  a  combined  moment'of  58  X  17  =  986,  show 
ing  a  difference  of  90 ;  consequently,  x  =  ^/(90*  5-OQO)  = 

o,532.5 

5.03  inches  =  required  diameter  of  pin. 

Such  would  be  the  result  as  to  stress  and  required 
diameter  of  pin,  provided  the  pin  remain  perfectly 
straight.  It  is  true  that  the  spring  of  the  pin  in  the 
direction  of  the  greater  moment,  or  sum  of  moments, 
will,  in  practice,  produce  an  obliquity  in  its  direction 
through  the  eyes,  which  will  throw  the  centres  of  bear 
ing  upon  the  pin,  nigher  to  the  adjacent  sides  of  the 
eyes,  and  thus  reduce  the  difference  of  opposite  mo 
ments,  and  consequently,  the  stress  upon  the  pin.  But 
such  relief  to  the  pin  must  be  attended  with  a  disturb 
ance  of  the  central  and  uniform  strain  of  the  chord 
bar ;  the  strain  being  brought  near  one  side  of  the  bar. 
Moreover,  as  this  can  only  result  from  actual  springing 
of  the  pin,  there  must  inevitably  be  a  degree  of  relaxa- 


224  BRIDGE  BUILDING. 

» 

tion  of  the  outside  link,  whenever  the  pins  at  its  two 
ends  are  deflected  toward  one  another.  On  the  con 
trary,  an  outside  link  or  bar  connecting  with  two  pins 
springing  from  one  another,  is  necessarily  subjected  to 
greater  strain  than  those  nighor  the  centres  of  pins,  in 
the  same  panel. 

In  this  case,  the  forces  tend  to  spring  the  pins  toward 
one  another  at  the  ends,  whence  the  outside  link"  must 
suffer  more  or  less  relaxation. 

It  seems  unnecessary  to  carry  these  examples  further. 
The  above  results  show  a  decided  advantage  in  the  ob 
lique  position  of  links,  diverging  toward  the  centre  of 
the  span,  so  as  to  have  the  inside  link  opposed  to  the  • 
diagonal. 

The  arrangement  of  links,  or  eye  bars,  here  assumed, 
and  the  amount  of  stress  assigned  to  them,  are  no  ex 
aggeration  upon  what  has  been  put  in  practice.  But 
the  preceding  calculations  must  be  sufficient  to  demon 
strate  the  exceptionable  character  of  such  practice. 
Two  links  upon  a  side  (4  to  the  panel),  after  two  or 
three  panels  next  the  end,  so  thin  as  not  to  occupy 
an  unnecessary  length  of  pin  —  each  taking  hold  of 
the  pin  outside  of  the  succeeding  one  toward  the  cen 
tre  of  the  truss,  may  be  admissible.  But  a  greater 
number,  in  the  opinion  of  the  author,  for  reasons  al 
ready  given,  is  not  to  be  recommended. 

DOUBLE  CHORD. 

CXXV.  To  obviate  the  difficulty  attending  the  use 
of  the  multiplex  chord,  consisting  of  many  links  in  a 
panel,  we  may  make  use  of  what  may  be  distinguished 
as  a  Double  Chord. 

We  have  seen  [LVI],  that  in  double  cancelated  trusses 
with  vertical  members,  there  are  two  independent  sets 


DIFFERENT  MODES  OF  CONSTRUCTION.         225 

of  diagonals  and  verticals,  which  have  no  interchange 
of  action  between  one  another.  Now,  each  of  these 
sets  may  have  its  own  lower  chord,  also  acting  inde 
pendently,  each  of  the  other,  but  uniting  at  the  same 
point  at  the  foot  of  the  king  brace,  which  is  common 
to  both  sets  of  web  members. 

In  such  case,  the  two  chords  (which  we  may  call  sub- 
q/ior^s),  may  be  one  above  the  other,  and  composed  of 
links  or  eye-bars,  extending  horizontally  across  two 
panels ;  the  links  or  bars  of  one  sub-chord  connecting 
opposite  the  centre  of  those  in  the  other,  and  the  up 
rights  in  one  set,  being  as  much  longer  than  those  in 
the  other,  as  the  distance,  vertically,  between  the  up 
per  and  lower  sub-chords. 

By  this  means,  about  one-half  of  the  extra  material 
in  chord  connections  would  be  saved;  and  a  more  uni 
form  stress  upon  the  chord  bars  secured,  than  would 
be  practicable,  even  with  4  links  acting  upon  one  con 
necting  pin. 

DETACHED,  AND  CONCRETE  PLANS  OF  CONSTRUCTION. 

CXXVI.  In  the  plan  of  Trapezoidal  truss  had  under 
consideration  in  the  last  few  preceding  sections,  the 
several  members  are  formed  in  separate  pieces,  to  be 
erected  in  place,  and  connected  by  screws,  bolts,  con 
necting  pins,  &c.,  as  the  parts  of  wooden  bridges  and 
building  frames  are  erected,  after  being  framed  and 
prepared,  each  for  its  particular  place. 

There  is  another  mode  of  construction,  in  which 
members  and  parts  of  members  are  permanently  riveted 
together  in  place;  or,  in  case  of  small  bridges,  the 
whole  structure  is  permanently  put  together  at  the 
manufactory,  and  transported  by  water  or  rail  to  the 
place  of  erection  and  use.  The  former  of  these  may 
29 


226  BRIDGE  BUILDING. 

be  called  the  detached,  and  the  latter,  the  concrete  mode 
of  construction. 

The  detached  plan  is  probably  the  best  adapted  to 
wrought  and  cast  iron  bridges,  and  also,  at  least,  equally 
adapted  to  bridges  entirely,  or  essentially  constructed 
of  wrought  iron,  when  vertical  thrust  uprights  are  em 
ployed. 

But  it  can  hardly  be  regarded  as  advisable  to  con 
struct  iron  bridges  with  independent  members,  without 
thrust  verticals.  For,  although  as  we  have  seen,  [XLVI,] 
the  latter  plan  shows  a  trifle  less  action  upon  the  ma 
terial  than  the  plan  with  verticals,  the  oblique  thrust 
members  in  the  web,  are  40  or  50  per  cent  longer  (ac 
cording  to  inclination),  as  well  as  being  in  greater 
number,  and  sustaining  less  average  action  to  the  piece. 

The  7  panel  truss,  Fig.  12,  has  4  compression  verti 
cals,  liable  to  an  average  action  of  8w" ;  while  truss 
Fig.  13,  has  not  less  than  6  diagonals,  liable  to  an 
average  compression  of  -±w"  \/2  (when  the  inclination 
is  45°),  equal  to  5.65i0".  In  the  mean  time,  these 
members  being-  over  40  per  cent  longer,  and  sustain 
ing  only  about  the  same  aggregate  amount  of  action, 
can  not  be  so  economically  proportioned  to  perform 
their  required  labor,  when  acting  independently,  as 
the  fewer  and  shorter  uprights. 

Still,  the  Trapezoid  with  individual  members  is 
practicable,  probably  with  about  the  same  economy  of 
material  without  verticals  as  with  them  ;  and,  if  it  be 
deemed  expedient  to  adopt  the  former,  the  modes  of 
forming  and  connecting  the  various  parts  may  be  so 
nearly  like  those  already  described  for  the  latter,  that 
particular  specifications  will  not  be  given  in  this  place. 

The  essential  conditions  to  be  observed,  are,  besides 
proportioning  the  parts  to  the  kind  and  degree  of  strain 


DIFFERENT  PLANS  OF  CONSTRUCTION.          227 

to  which  they  may  be  exposed,  to  see  that  the  forms 
of  diagonals  liable  to  compresaive  action,  be  made 
capable  of  withstanding  such  action,  according  to  the 
table  of  negative  resistances  [xcin] ;  and,  that  those 
liable  to  a  change  of  action  from  tension  to  compres 
sion,  and  the  contrary,  be  formed  and  connected  in  such 
manner  as  to  enable  them  to  act  in  both  directions. 

CXXVII.  In  the  concrete,  or  rivet  work  plan  of 
construction,  the  Trapezoid  without  verticals  may,  it 
is  thought,  be  generally  adopted  with  advantage. 
Upon  this  branch  of  the  subject,  however,  but  little  of 
detail  will  be  attempted  at  this  time,  the  author  having 
had  very  little  direct  practical  experience  in  the  pre 
mises. 

The  first  point  to  be  attended  to,  of  course,  as  in  all 
cases  of  bridge  construction,  is,  to  arrange  the  general 
outline  and  proportions  of  the  truss ;  that  is,  the  num 
ber  of  panels,  and  depth  of  truss  suitable  for  the  par 
ticular  case  in  hand.  This  being  done,  the  amount 
and  kind  of  force,  whether  thrust  or  tension,  to  which 
each  part  is  liable,  should  be  determined ;  for  which 
purpose,  the  value  of  w,  and  of  w'  (the  variable  and 
constant  panel  load  for  the  truss),  must  be  assumed,  or 
estimated  according  to  the  best  data  at  command  ; 
when  the  stresses  of  the  several  parts  are  readily  ob 
tained  by  process  already  explained;  [XLIV,  &c.]. 

We  are  then  prepared  to  assign  the  requisite  cross- 
section  to  each  part,  and  to  adopt  a  suitable  form  of 
bar,  or  combination  of  bars  and  plates,  for  each  mem 
ber.  Thrust  members  will  usually  (if  long),  be  formed 
of  several  parts,  mostly  flat  plates,  angle  iron,  T  iron, 
and  channel  iron,  united  by  riveting  in  such  form  of 
cross-section  as  may  give  the  largest  diameter  practi- 


2:23  BRIDGE  BUILDING. 

cable  without  too  much  attenuation  of  the  thickness 
of  material,  a  point  upon  which  no  certain  rules  can  be 
given. 

Flat  plates,  when  connected  by  riveting  at  the  edges, 
may  be  of  a  width  of  30  to  40  times  the  thickness  per 
haps,  without  liability  to  "  buckle"  under  reasonable 
compression.  When  riveted  along  the  centre,  a  width 
of  12  to  20  times  the  thickness,  will  be  in  better  pro 
portion. 

UPPER  CHORD. 

CXXYIII.  A  good  upper  chord  may  be  made  in 
rectangular,  or  box  form,  of  flat  plates  and  angle  iron  ; 
or,  for  small  bridges,  of  channel  iron,  with  flanges 
either  inward  or  outward,  upon  the  two  vertical  sides, 
with  flat  plates  upon  upper  and  under  sides  ;  the  upper 
riveted,  and  the  lower  one  either  riveted,  or  put  on 
with  screws,  tapped  into  the  lower  flanges  of  the 
channel  bars. 

The  upper  plate,  when  flanges  turn  inward,  may 
project  half  an  inch,  or  an  inch,  and  the  lower  one, 
come  even  with  the  sides.  The  channel  bars  should 
meet  at  the  nodes,  or  connecting  points,  and  a  splice 
plate  covering  the  joint  may  project  below  the  chord 
far  enough  to  form  a  connection  with  diagonals  by 
riveting.  (Fig.  44). 

Diagonals  acting  by  tension  only,  may  be  plain  flat 
bars  of  width  from  8  to  10  times  the  thickness.  Those 
acting  by  thrust  principally,  may  be  of  T  iron  with 
short  diagonal  bars  riveted  to  the  mid  rib,  (e  Fig.  44), 
giving  a  width  corresponding  with  that  of  the  upper 
chord,  or  with  the  space  between  tension  diagonals, 
so  that  the  latter  may  be  riveted  to  the  cross-plate  of 
the  T  iron  at  the  crossings,  to  give  lateral  support  to 


RIVET- WORK  BRIDGES. 


229 


the  thrust  members.     Angle  iron  may  also  be  used  in 
stead  of  T  iron,  in  these  members. 


FIG.  44. 


\ 

o 

0 

0    0 

1 

c 

o    o 

o 

1 

O 
O 

o 

o 

o. 

J 

0 

"6  o 

O   0 

3 

Diagonals  acting  by  both  thrust  and  tension,  should 
be  formed  and  connected  with  reference  to  the  forces 
they  are  liable  to. 

For  small  bridges,  small  plain  I  bars  may  be  used 
for  thrust  diagonals  with  advantage. 

In  all  cases  of  tension,  rivets  should  be  so  arranged 
when  practicable,  as  to  leave  all  the  section  available, 
except  the  diameter  of  a  single  rivet  hole;  that  is, 
no  section  through  two  or  more  holes,  including  the 
one  farthest  from  the  end,  should  have  less  area  than, 
a  square  section  through  one  hole,  [cxvii,  Fig.  31.] 

In  Fig.  44,  a,  a,  &c.,  represent  tension  diagonals,  of 
plain  flat  bars,  with  cross-section  proportioned  to  the 
stress  in  each  case;  6,6  —  thrust  diagonals  of  T  iron 
and  short  diagonal  plates,  as  seen  at  e ;  c,  e,  the  upper, 


230  BRIDGE  BUILDING. 

and  <f,  the  lower  chord  ;  the  dotted  line  J,  shows  the 
meeting  of  lower  chord  plates,  about  4  inches  toward 
the  abutment  from  the  point  of  meeting  of  the  several 
centres  of  chord  and  diagonals.  The  side  plates  of  up 
per  chord  may  meet  at  the  centre  of  the  node,  or  con 
necting  point. 

The  upper  splice  plates  are  of  irregular  form  (or,  they 
may  be  cut  on  a  regular  slant  from  upper  to  lower 
angle),  but  such  as  to  cut  without  waste  of  iron.  They 
may  be  clipped  out  upon  the  under  side,  as  by  the 
curved  line,  or  not,  as  may  be  preferred. 

The  lower  splice  plates  may  be  rectangular,  and  of 
such  length  and  width  as  to  admit  of  a  sufficient  num. 
ber  of  rivets,  properly  arranged,  to  be  equal  in  strength 
to  the  net  section  of  chord  plate  and  diagonals. 

It  is  scarcely  necessary  to  repeat,  that  rivet  section 
connecting  two  thicknesses  of  plate  only,  should  exceed 
the  net  section  of  plate  by  as  much  as  the  direct  tensile 
strength  exceeds  the  shear-strength  of  iron. 

LOWER  CHORD. 

CXXIX.  The  following  plan  of  a  flat  plate  bottom 
chord  adapted  to  a  connection  of  diagonals  by  connect 
ing  pins,  is  transcribed  from  the  author's  former  work ; 
and,  by  widening  the  splice  plates,  as  in  Fig.  44,  ia 
equally  adapted  to  the  concrete  mode  of  construction  ; 
i.  e.,  by  rivet  work. 

The  plan  contemplates  each  half-chord  as  composed 
of  two  courses  of  plates  (except  near  the  ends),  spliced 
alternately,  one  at  each  node  so  as  to  "  break  joints." 
The  two  half  chords  are  to  be  placed  at  such  distance 
apart  as  to  accommodate  the  connections  with  dia 
gonals,  and  with  uprights,  when  used  in  connection 
with  uprights. 


RIVET- WORK  BRIDGES.  231 

For  a  16  panel  truss,  as  arranged  in  Figures  18  and 
19.  Suppose  w  =  12m  (m  representing  l,0001bs.) ;  w'  — 
4w,  and  W  =  16w,  =  w  -f  w' ;  —  diagonals  (except  the 
steep  ones),  inclining  45°. 

The  end  brace,  then,  sustaining  7JW  =  120w,  [LVI], 
produces  tension  equal  to  60/n,  upon  the  first  and 
second  section  of  chord,  in  Fig.  18,  the  proportions  for 
which  will  be  here  considered.  Allowing  then,  10m 
to  the  square  inch,  each  half  chord  requires  a  plate  of 
about  8"  byrV,  up  to  the  second  node  from  the  end. 

This  plate  may  extend  —  say  within  8"  of  the  centre 
of  the  connecting  pin  at  the  2d  node,  where  it  may  be 
connected  with  a  |"  plate,  by  two  splice-plates  about 
27"  long  (see  A.  Fig.  45),  with  a  net  section  equal  to 
the  yy  plate,  or,  say  J"  thick.  Fig.  45,  exhibits  a 
disposition  of  rivet  and  pin  holes,  at  A,  so  arranged  as 
to  preserve  the  full  section  of  plates,  less  the  diameter 
of  a  single  V  rivet  hole. 

Or,  the  splice-plates  maybe  1"  shorter,  and  J  thicker, 
and  the  two  rivets  next  the  joint  (j),  on  either  side, 
opposite  one  another,  as  at  BB,  Fig.  45 ;  thus  giving 
the  same  section  (of  splice-plates),  through  two  opposite 
rivets  in  the  thicker,  as  through  one  rivet  in  thinner 
and  longer  splice  plates.  In  this  case,  the  joint  should 
be  4|"  from  centre  of  connecting  pin  (p),  and  a  little 
more,  when  the  rivets  exceed  V  in  diameter. 

At  the  third  node,  an  increase  of  section  is  required, 
and  a  f"  plate  may  be  added  on  the  inside,  lapping  9 
or  10  inches  back  of  the  pin,  with  a  J"  splice  plate  of 
the  B  pattern  to  balance  the  extra  inch  in  width  re 
quired  for  opposite  rivet  holes,  and  a  2"  pin  hole. 

The  inside  plate  continuing  past  the  next,  or  4th 
node,  the  f"  outside  plate  may  be  met  by,  and  spliced 
to  a  |"  plate,  in  either  of  the  modes  indicated  by  A  and 


BRIDGE  BUILDING. 

B,  Fig.  45.  On  plan  B,  the  outside  splice  plate  should 
be  at  least  J"  thick,  and  the  inside  one,  T5g".  In  this, 
as  in  other  cases  where  a  thinner  plate  meets  a  thicker 
one,  the  former  is  to  be  furred  out  to  the  thickness  of 
the  latter. 

At  the  5th  node,  the  outside  plate  may  continue, 
•while  the  inside  one  is  succeeded  by  a  f"  plate,  with  a 
£"  splice-plate  inside,  and  one  of  TV'  thickness  upon 
the  outside ;  splice-plates  in  all  cases  being  intended 
to  be  upon  the  outside,  and  not  between  the  two  courses 
of  plates  forming  the  half  chord. 

The  same  general  process  being  continued,  each 
course  being  spliced  at  alternate  nodes,  and  breaking 
joints  with  one  another,  we  introduce  in  the  outside 
course,  a  V  plate  from  the  6th  node  to  the  centre 
of  the  chord,  and  a  J"  plate  from  the  7th  node,  past 
the  centre  to  the  9th  node,  and  so  on,  with  a  reversed 
order  of  succession  to  the  other  end  of  the  chord. 

The  two  1"  plates  in  the  outside  course,  should  meet 
at  the  centre  connecting  pin,  and  all  other  joints  should 
be  a  few  inches  from  the  pin,  on  the  side  toward  the 
end  of  the  chord,  as  in  diagram,  Fig.  45. 

FIG.  45. 


O    I 


Each  pair  of  splice  plates  should  have  a  minimum 
net  section,  together  with  the  net  section  of  the  con 
tinued  plate,  at  least  equal  to  the  sections  of  the  con 
tinued,  and  the  thinner  spliced  plate,  through  one  of 
the  smaller  rivets  used  in  the  splice ;  and  the  relative 
thickness  of  the  two  splice  plates  should,  as  nearly 


RIVET- WORK  BRIDGES.  233 

as  practicable,  be  inversely  as  the  respective  distances 
of  their  centres  from  the  centre  of  the  spliced  plate. 

For  illustration  ;  at  the  6th  node,  the  continuous 
plate  is  |",  and  the  thinner  spliced  plate  J",  making  in 
the  two,  a  thickness  of  1J",  by  T1  for  the  net  width ; 
giving  a  section  of  10J  square  inches.  This  splice  re 
quiring  1J"  rivets  next  the  joint,  to  give  the  necessary 
rivet  section,  the  net  width  of  splice  plates  and  con 
tinuous  plate  through  two  opposite  \\"  rivets,  is  only 
5J".  Consequently,  the  aggregate  thickness  required 
to  give  10J  square  inches,  is  about  1.91"  ;  and,  deduct 
ing  0.625"  for  the  continuous  plate,  we  have  1.285" 
for  thickness  of  the  two  splice-plates. 

Then,  representing  thickness  of  spliced  plate  by  a 
(disregarding  the  furring  plate,  or  including  it  in  the 
quantity  a),  that  of  the  continuous  plate  by  6,  that  of 
the  two  splice-plates  by  c,  and  that  of  the  thicker  one 
by  x;  we  form  the  following  equation,  as  will  be  ob 
vious  on  reference  to  Fig.  46,  which  is  an  edge  view 
of  splice  at  node  6. 

xx  J  (a+x)  =  (c — x)  X  (b+ J  (a+c — x) ;  whence,  the 
formula  x  =*  c  x  (a+2b+c)  H-  2  (#+b  +  c). 

This  formula  applied  to  the  case  represented  in  Fig. 
46,  gives  x  =  0.7804",  and  c— x  =  0.5046". 

FIG.  40 

, «•     «•»  I    !   ^ <™,     ^.    «•• — , 


The  letter  a  in  the  diagram  shows  the  splicing  of  a 
1"  with  a  £"  plate,  the  thickness  being  equalized  by  a 
furring  plate. 

Figure  46  gives  also,  a  general  idea  of  the  splices  pro 
posed  for  this  kind  of  chord,  in  case  of  the  adoption  of 
30 


234  BRIDSE  BUILDING. 

the  short  splice  plates  and  opposite  rivets,  aa  seen  at 
BB,  Fig.  45.  p  indicates  the  connecting  pin  (which,  in 
the  concrete  plan  of  construction  should  be  replaced 
by  two  opposite  rivets,  as  seen  in  Fig.  44),  having  a 
cross-section  in  the  parts  passing  through  the  chord 
plates,  about  equal  to  that  of  one  of  the  two  main  dia 
gonals  connecting  with  each  pin  respectively,  at  the 
several  nodes. 

The  body  of  the  pin  between  chord  plates,  should 
have  lateral  stiffness  enough  to  withstand  the  stress 
produced  by  diagonals  horizontally,  estimated  upon 
the  principles  of  the  lever,  which  will  be  greater  as  the 
distance  of  diagonals  from  chord  plates  is  greater,  and 
the  contrary.  If  the  bearing  of  the  upright  upon  the 
pin  be  between  the  diagonals  and  the  chord  plates,  as 
by  a  bi-furcation  like  that  at  the  upper  chord  (see  a 
Fig.  38)  the  body  of  the  pin  will  usually  require  a 
section  about  equal  to  that  of  the  two  main  diagonals 
connected  with  it.  But  this  is  no  certain  rule. 

The  ends  of  the  connecting  pin  should  extend  through 
the  chord  plates  so  as  to  receive  a  thin  nut  upon  each 
end,  and  also  the  eyes  of  sway  rods  upon  the  inside 
end,  in  case  that  mode  of  connection  be  adopted  for 
those  parts. 

In  the  case  of  trusses  without  verticals  constructed 
in  rivet  work,  the  best  balanced  action  will  be  secured 
by  connecting  diagonals  between  the  splice  plates,  by 
means  of  rivets  through  both,  thus  bringing  each  dia 
gonal  bar  directly  over  each  half  chord,  and  producing 
uniform  stress,  as  nearly  as  is  practicable.  When  dia 
gonal  bars  do  not  fill  the  space  between  splice-plates, 
the  deficiency  may  be  made  up  by  furring  plates,  or 
thimble  rings. 


RIVET- WORK  BRIDGES.  235 

Tension  diagonals  will  usually  require  from  25  to  33 
per  cent  of  extra  section  to  make  up  the  loss  in  rivet 
holes.  In  thrust  diagonals,  no  allowance  need  gene 
rally  be  made  for  rivet  holes,  as  rivets  properly  distri 
buted,  will  not  impair  the  efficiency  of  the  member  in 
withstanding  compression. 

With*  regard  to  the  relative  merits  of  this  kind  of 
lower  chord,  k  requires,  in  the  proportions  above  as 
sumed,  namely,  8"  width  of  plates  and  1"  diameter  of 
the  smaller  rivets,  about  14  per  cent  of  extra  section 
on  account  of  rivet  holes,  through  the  whole  length. 
For  splice  plates  and  rivets,  at  least  an  equal  amount 
should  be  allowed,  making  28  per  cent  for  waste  ma 
terial,  over  and  above  the  net  available  length  and 
cross-section.  The  corresponding  waste  in  the  link 
chord,  and  in  the  eye-plate  chord  [cxiv],  can  scarcely 
exceed  10  per  cent,  when  the  connections  are  made 
with  wrought  iron  pins. 

Hence,  the  advantage  as  to  economy  of  material, 
seems  decidedly  in  favor  of  the  latter  plans ;  and  the 
cost  of  manufacture  can  hardly  be  estimated  in  favor 
of  the  former.  If  the  riveted  chord,  then,  have  any 
claim  to  favor  and  preference,  it  is  mostly  owing  to 
the  fact,  that  being  manufactured  cold,  it  escapes  the 
deteriorating  effects  frequently  resulting  to  iron  in  the 
process  of  forging  and  welding,  and  the  risk  of  flaws, 
and  imperfect  cohesion  of  the  welded  surfaces. 

How  far  this  consideration  should  be  regarded  as  an 
offset,  or  an  overbalance  to  15  or  20  per  cent,  of  ma 
terial  lost  in  rivet  holes  and  splices,  further  experience 
and  observation  alone  can  probably  determine. 


236  BRIDGE  BUILDING. 

SWAY  BRACING. 

CXXX.  The  primary  and  essential  purpose  of  a 
bridge  is,  to  withstand  vertical  forces  which  are  certain, 
and,  to  a  large  extent,  determinate  in  amount.  ~W"e 
can  estimate  nearly  the  weight  of  a  train  of  rail  road 
cars,  a  drove  of  cattle,  or  a  crowd  of  people  ;  and  the 
amount  of  material  required  to  sustain  them. 

But  the  lateral,  ar  transverse  forces  to  which  a 
bridge  superstructure  is  liable,  are  of  a  casual  nature, 
depending  upon  conditions  of  which  we  have  only  a 
vague  and  general  knowledge  ;  and,  can  not  predeter 
mine,  their  effects  with  any  considerable  degree  of 
certainty. 

We  know  full  well  from  experience,  that  it  is  always 
expedient  to  provide  every  bridge  superstructure  with 
means  of  support  against  transverse  horizontal  forces  ; 
and  we  introduce  certain  parts  and  members  for  that 
express  purpose.  These  have  been  frequently  alluded 
to  heretofore  in  this  work,  under  the  designation  of 
sway  rods,  lateral  ties,  or  lateral  braces.  But  no  attempt 
has  ever  been  made,  to  the  author's  knowledge,  to 
point  out  the  proper  sizes  and  proportions  of  such 
members,  upon  any  determinate  principles  or  data. 

In  this  respect,  reliance  has  mostly  been  placed  upon 
"judgment,"  and  general  observation  as  to  precedent 
and  common  practice ;  as  was  the  case  in  fact,  with 
regard  to  bridge  construction  generally,  until  within 
the  last  twenty-five  or  thirty  years.  Within  this 
period,  and  since  the  extensive  use  of  iron  in  bridge 
construction  has  been  introduced,  more  attention  has 
been  given  to  scientific  principles,  in  adjusting  the  pro 
portions  of  the  several  parts  and  members  designed  to 
withstand  the  effects  of  vertical  pressure. 


SWAY  BRACING.  237 

The  modern  bridge  builder,  if  he  has  been  properly 
educated  for  his  business,  having  arranged  the  outline 
of  his  truss,  makes  his  computations,  and  marks  upon 
each  line  of  his  diagram,  so  many  thousand  pounds  of 
tension  upon  this,  so  many  tons  of  compression  upon 
that,  and  so  much  shear  strain,  or  lateral  strain  upon 
each  rivet,  connecting  pin,  or  beam,  and  assigns  to 
each  place  a  member  containing  such  an  amount,  and 
such  a  kind  of  material,  as  experience  has  proved  to 
be  sufficient  to  sustain  the  given  stress  with  safety. 

Thus  far,  his  course  is  scientific  and  sensible.  But  in 
arranging  his  system  for  securing  lateral  stability  and 
steadiness,  science  can  lend  him  but  little  assistance. 

He  knows  the  wind  will  blow  against  the  side  of  his 
structure  ;  but  whether  with  a  maximum  force  of  one 
hundred  pounds,  or  as  many  thousands,  he  has  no 
means  of  knowing  with  any  considerable  degree  of 
certainty,  or  probability. 

He  knows,  furthermore,  that  every  deviation  from  a 
straight  line  by  a  body  passing  over  and  upon  a  bridge, 
even  to  changing  the  weight  of  a  pedestrian  from  one 
foot  to  the  other  (unless  his  steps  be  directly  in  front 
of  one  another,  and  this  could  hardly  form  an  excep 
tion),  is  attended  by  more  or  less  tendency  to  lateral 
swaying  of  the  structure. 

Every  inequality  in  the  line  of  a  rail  road  track, 
laterally  or  vertically,  unless  both  rails  have  precisely 
the  same  vertical  deviation,  produces  a  transverse  mo 
tion  in  the  centre  of  gravity  of  the  load,  and  conse 
quently  a,  lateral  sway  in  the  structure.  The  passage 
of  a  carriage  wheel  over  a  stick  or  a  pebble,  raising 
one  wheel  above  the  opposite  one,  changes  the  centre 
of  gravity  of  the  load  to  the  right  or  left,  and  impels 
the  structure  in  the  opposite  direction. 


288  BRIDGE  BUILDING. 

These  are  some  of  the  external  causes  generating 
transverse  action,  and  motion  of  the  structure.  But 
in  addition  to  these,  the  upper  chord  itself,  acting  by 
thrust,  is,  at  best,  in  unstable  equilibrio,  and  liable  at 
all  times  to  exert  more  or  less  transverse  action,  and, 
if  not  kept  in  line  by  an  efficient  system  of  transverse 
bracing  or  tying,  will  lose  its  equilibrium,  and  be  de 
prived  of  the  power  of  performing  its'  appropriate 
functions  in  the  structure. 

Now,  these  disturbing  lateral  forces  are  quite  small, 
compared  with  the  vertical  action  upon  the  trusses  ; 
and,  the  vertical  strength  of  the  truss  does  not  neces 
sarily  imply  any  power  of  resistance  transversely  ;  the 
tendency  of  the  lower  chord  to  preserve  a  straight  line, 
being  essentially  balanced  by  that  of  upper  chord  or 
arch  to  buckle  laterally;*  provided  the  chords  be  so 
dependent  upon  one  another  that  both  must  sway  to 
the  right  or  left  at  the  same  time. 

Hence,  it  is  always  expedient  to  provide  some  es 
pecial  means  for  counteracting  these  lateral  forces, 
•which  is  usually  done  by  the  introduction  of  a  system 
of  horizontal  diagonal  ties  or  braces  (small  iron  rods 
in  iron,  and  the  same,  or  timber  braces,  in  wooden 
bridges),  below  the  track  or  platform,  in  the  horizon 
tal  panels  formed  by  consecutive  beams,  and  the  chords 
of  opposite  trusses.  Also,  when  trusses  are  sufficiently 
high,  diagonals  and  cross-struts  are  introduced  between 
upper  chords,  to  prevent  lateral  buckling. 

No  attempt  will  here  be  made  to  assign  specific 
stresses  as  liable  to  occur  in  sway  rods  or  braces, 
based  upon  calculations  from  the  uncertain  and  in 
determinate  elements  upon  which  the  lateral  action  upon 

*  The  only  truss  known  to  the  author,  not  liable  to  this  lateral  buck 
ling,  is  the  W hippie  Independent  arch  truss,  shown  in  Fig.  27. 


SWAY  BRACING.  239 

bridges  depends.  Bat,  judging  from  experience  and 
observation,  it  may  be  recommended  that  iron  sway- 
rods  be  made  of  iron  not  less  than  f  inch  in  diameter, 
for  bridges  of  five  panels  or  under,  f  inch  from  six  to 
ten  panels,  inclusive.  For  twelve  and  fourteen  panels, 
f  inch  for  ten  middle  panels,  and  {  inch  for  the  rest ; 
and,  for  sixteen  the  same  as  last  above,  with  the  ad 
dition  of  a  pair  of  1  inch  rods  in  the  end  panels. 

These  are  the  least  dimensions  recommended  (in  all 
cases  exclusive  of  screw  thread),  for  ordinary  bridges 
with  panels  not  much  exceeding  10  feet.  For  panels 
approaching  or  exceeding  12  feet,  J-  inch  may  properly 
be  added  to  the  above  specified  diameters  generally. 

If  upper  sway  rods  connect  in  the  middle  of  cross- 
struts,  with  a  longitudinal  reach  across  two  panels,  [see 
cxx,  and  Figs.  38  and  39],  they  may  safely  be  made 
smaller  than  when  they  cross  one  panel  only. 

The  action  of  wind  is  nearly  a  uniform  pressure  from 
end  to  end  of  the  structure,  and  causes  mu<jh  the  same 
progressive  increase  of  stress  upon  sway-rods,  as  the 
weight  of  structure  and  uniform  load  produces  upon 
diagonals  in  the  trusses  —  a  fact  which  was  recognized 
in  assigning  larger  sway-rods  at  and  near  the  ends  of 
long  bridges.  But  the  casual  impulses  resulting  from 
unevenuess  in  track  or  platform,  giving  slight  lateral 
movement  to  passing  loads,  and  acting  at  single  points 
here  and  there,  this  way  and  that,  do  not  produce  an 
accumulation  of  effect  toward  the  ends.  Hence,  as  it 
regards  withstanding  the  latter  forces,  no  variation  in 
sizes  of  sway-rods  is  required. 

CXXXI.  Sway-rods  acting  by  tension  would  ob 
viously  draw  the  opposite  chords  toward  one  another, 
but  for  the  resistance  of  transverse  beams  or  struts, 


240  BRIDGE  BUILDING. 

while  they  also  exert  a  longitudinal  action  npon  the 
chords,  thereby  increasing  or  diminishing  the  stress 
npon  chords,  due  to  the  action  of  structure  and  load. 
Chords,  however,  are  usually  proportioned  without 
provision  for  increase  of  stress  liable  to  accrue  from 
action  of  sway-rods;  and,  from  the  small  sizes  of  the 
latter,  as  compared  with  the  former,  and  the  obliquity 
of  their  action,  seldom  expending  more  than  half  their 
direct  stress  npon  the  chords  longitudinally,  this  small 
action  may  be  neglected,  as  forming  one  of  the  con 
tingencies  for  which  a  large  surplus  of  material  is  al 
ways  provided  in  chords,  over  what  is  actually  required 
to  withstand  the  effects  of  any  probable  vertical  action. 

Certain  modes  of  inserting  and  connecting  sway-rods 
have  been  previously  alluded  to,  sometimes  with  the 
beams  by  means  of  eyes  and  bolts  [cviri,  Figs.  31 
and  33],  and  sometimes  more  directly  with  the  chords 
[cxix,  Fig.  35,  d,  and  Fig.  39,  d.'] 

The  best  connection  is  that  which  gives  the  nearest 
approximation  to  central  and  uniform  action  upon  all 
parts  of  the  chord,  and  also  of  the  beam  or  strut.  The 
plan  described  in  section  cxx,  and  seen  in  Fig.  37,  when 
admissible,  affords  a  good  connection  for  bottom  sway 
rods. 

Undoubtedly  there  may  be  better  devices  for  the 
purpose  under  consideration,  as  well  as  for  other  de 
tails,  than  any  that  have  occurred  to  the  author.  But 
such  as  are  herein  described  have  mostly  been  put  in 
successful  practice,  and  are  thought  not  to  be  seriously 
faulty. 


COMPARISON  or  PLANS.  241 


COMPARISON  OF  DIFFERENT  PLANS  OF 
IRON  TRUSS  BRIDGES. 

CXXXIL  It  is  the  purpose  of  this  chapter  to  can 
vass  the  relative  merits  of  most  of  the  several  systems 
of  IRON  BRIDGE  TRUSSING,  which  have  claimed  and  re 
ceived  more  or  less  of  public  notice  and  approval  during 
the  last  few  years  ;  and  of  which  the  distinctive  princi 
ples  have  already  been  discussed  in  preceding  pages  ; 
though  not  in  the  precise  combinations  here  about  to 
be  presented. 

We  may  take  the  number,  lengths  and  stresses  (the 
latter  governing  principally  the  required  cross-sections), 
of  the  several  long  pieces  or  members  of  the  truss,  in 
the  manner  employed  in  the  fore  part  of  this  work,  as 
affording  a  near  criterion  of  the  comparative  cost  and 
economy  of  the  bridges  respectively.  Then,  after  re 
ference  to  such  peculiarities  as  may  seem  advantageous 
or  otherwise,  leave  the  reader  to  his  own  conclusions 
in  regard  to  the  relative  merits. 

TKE  BOLLMAN  TRUSS,  Fia.  47, 

Is  founded  upon  the  general  principle  discussed  in 
sections  xxn  and  xxm,  with  oblique  tension  rods,  and 
a  thrust  upper  chord,  in  place  of  the  thrust  braces  and 
tension  lower  chord  as  represented  in  Fig.  9. 

Let  Fig.  47,  represent  a  truss  15'  high,  and  100'  long ; 
or,  in  the  proportion  of  1  to  6f .  Also,  let  w  represent 
the  maximum  variable  load  for  each  of  the  points  c,  d, 
e,  etc.,  and  w'(say,=  Jw),  the  permanent  weight  of 
one  panel  of  superstructure,  supposed  to  be  constantly 
bearing  at  each  of  said  points.  Then  making  "W"  = 
w  X  w',  we  have  JW  =  weight  sustained  by  ac. 
31 


242  BRIDGE  BUILDING. 

How,  we  have  seen  [vn],  that  the  stress  upon  an 
oblique  in  such  case,  equals  the  weight  sustained,  mul 
tiplied  by  the  length,  and  divided  by  the  vertical  reach 
of  the  oblique  ;  and,  assuming  that  the  member  requires 
a  cross-section  proportional  to  the  stress,  it  follows  that 
(making  ab  =  1),  the  amount  of  material  required  in  ac, 
will  be  as  the  weight  it  sustains,  multiplied  by  the 
square  of  its  length.  Hence,  the  material  required  in 
«<?,  must  be  as  f  W  X  a<:2.  Then,  diminishing  be  until 
ac  coincides  with  ab,  W  X  ab2  becomes  "W,  which  is 
still  proportional  to  the  material  required  in  ac  (which 
has  now  become  =  a&,  =  1),  and,  being  replaced  by  M, 
representing  the  actual  material  required  to  sustain  the 
weight  "W",  with  a  length  equal  to  ab  (our  unit  of  length), 
in  a  vertical  position,  we  have  only  to  substitute  M  X 
ac2  for  W  x  ac2r  to  know  the  actual  material  necessary 
to  sustain  the  weight  W  (at  a  given  stress  per  square 
inch  of  cross-section),  with  any  length  and  position, 
retaining  the  same  vertical  reach,  equal  to  unity. 

It  must  be  obvious,  therefore,  that  M,  with  the  co 
efficient  used  before  W,  to  express  the  weights  respect 
ively  sustained  by  the  several  oblique  rods  in  truss  47, 
will,  when  multiplied  by  the  squares  of  the  respective 
lengths  of  those  obliques,  show  the  amount.of  material 
required  in  their  construction,  under  the  conditions 
above  expressed. 

Let  m  =  JM,  and  A  =  be.  Then,  we  manifestly  have, 
for  material  in  the  14  obliques  of  the  truss  in  question 
7m  (#+!)+  6m  (4A2+1)  +  5m  (9A2+1)  +  4m  (16A2+1)  + 
3m  (25/ta+l)  +  2m  (36A2+1)  +  1m  (49A2+1)  =  (336A2+ 
28)m,  for  those  meeting  at  <7,  and  a  like  amount  for  those 
meeting  nil;  making  a  total  of  (672A2-f56)m.  But 
A2  =  0.694,  which  substituted  in  the  last  expression, 
gives  522.368m,  =  65.296M. 


COMPARISON  OF  PLANS.  243 

FIG.  47. 

BOLLMAN  TRUSS. 
q         p          o         n        m  I 


The  thrust  of  the  chord  al,  equals  the  horizonta. 
action  of  the  7  obliques  connected  with  cither  end. 
Making  then  x  =  JW,  and  h  =  6c,  ==  \bk,  it  is  obvious 
that  each  oblique  carries  weight  equal  to  x  x  the  number 
of  panels  not  crossed  by  it,  while  its  horizontal  reach 
equals  h  x  the  number  of  panels  it  does  cross.  -Hence, 
the  horizontal  action  of  each  oblique,  equals  hx  X  the  pro- 
duct  of  the  numbers  of  panels  at  the  right  and  loft 
respectively,  of  the  lower  end  of  the  oblique. 

The  compressive  force  acting  from  end  to  end,  upon 
al,  then,  must  be  equal  to  Ax  (7,  -f  2x6,  -f  3x5,  +  42-f 
5x3,  +  6x2,  +  7),  =  84Ax,  =  10jWx0.833,  =  8.75W. 

Multiplying  stress  by  length,  and  substituting  M,  we 
have  8.75  X  6.66M  ••  58  JM  =  material  required  in  «/,  at  a 
given  stress  per  square  inch  of  cross-section ;  M  being  the 
amount  required  for  a  unit  of  length  (a6),  to  sustain 
the  unit  of  weight  (W),  at  the  same  rate  of  stress. 

Add  7M  for  two  end  posts,  with  length  equal  to  1 
and  bearing  weight  equal  to  7W,  and  we  obtain  65  JM 
as  a  total  for  thrust  material  in  long  pieces,  not  includ 
ing  7  intermediate  uprights,  not  properly  to  be  class- 
fied  with  other  parts,  as  their  action  is  merely  incidental, 
except  that  of  supporting  the  weight  of  upper  chord. 

The  parts  above  considered,  mainly  determine  the 
character  of  the  truss  as  to  economy  of  material. 


244  BRIDGE  BUILDING. 

Other  parts,  such  as  short  bolts,  nuts,  connecting  pins, 
&c.,  although  just  as  essential,  are  comparatively,  of 
small  amount  and  cost,  except  the  intermediate  up 
rights,  which  will  be  referred  to  hereafter. 

If  the  truss  be  used  in  a  deck  bridge,  and  the  end 
posts  be  replaced  with  masonry,  the  intermediates 
will  sustain  the  same  weight  as  the  ends  sustain  in  a 
through  bridge,  thus  giving  the  same  representative  of 
material  as  above  found. 

THE  FINCK  TRUSS,  FIG.  48, 

CXXXIII.  Possesses  several  of  the  characteristics 
which  distinguish  the  Bollman  plan.  Both  dispense 
with  the  bottom  chord,  which  is  common  to  most,  if 
not  all  other  plans  of  truss,  for  both  iron  and  wooden 
bridges.  Both  also  employ  a  pair  of  tension  obliques 
acting  in  horizontal  antagonism  to  each  other,  at  each 
of  the  supporting  points  c,  d,  e,  &c.  But  while  in  the 
one,  the  members  of  each  pair  of  obliques  are  of  equal 
length  and  tension,  in  the  other,  the  pairs  consist  of 
unequal  members  (except  at  the  centre),  as  the  dia 
grams  will  sufficiently  illustrate. 

It  will  readily  be  seen  that  Fig.  48  exhibits  three 
classes  of  obliques,  consisting  respectively  of  2,  4,  and  8 
members  to  the  class.  Supposing  a  truss  of  the  same  di 
mensions  and  proportions,  and  subjected  to  the  same 
load,  as  in  case  of  Fig.  47,  and  using  the  same  notation, 
as  far  as  applicable;  it  is  manifest  that  each  of  the  8 
short  obliques,  sustains  J~W~.  The  4  next  longer  sus 
tain  upon  each,  a  weight  equal  to  W  -  one  half  directly, 
and  the  other,  through  the  short  obliques  and  uprights. 
The  two  long  obliques. sustain  2W  each,  being  the  half 
of  1\V,  received  directly  at/,  and  1  and  2  respectively 


COMPARISON  OF  PLANS. 


245 


through  the  upright,  from  members  of  the  other  classes, 
meeting  at  the  point  p. 

The  material  required  for  all  the  obliques,  then,  (ab 
being  =  1,  and  be  =  A),  is  8  X  J  (A2  +  1)  -f  4  X  1  (4/t2  -f 
1)  +  '2  x  2  (Iti/i2  -f  1)M,  being  the  number  of  pieces  in, 
each  class  multiplied  by  co-efficients  of  W  in  \veights 
sustained,  and  by  squares  of  length  respectively,  and 
the  sum  of  products  multiplied  by  M. 

Subsituting  in  the  above  expression  the  value  of  A2, 
(0.694),  and,  reducing  and  adding  terms,  we  derive 
material  in  obliques  =  70.296  M. 

FIG.  48. 

FINCK  TRUSS. 

asrqponml 


k 


The  compression  upon  the  chord  a  I,  is  equal  to  the 
horizontal  action  of  one  member  of  each  class  of  ob 
liques,  communicated  at  each  end  ;  that  is,  equal  to 
(i  h  -f  2/i  +  8/i) W,  =  10J  h  W  ;  and,  multiplying  by 
length  (  =  6.66),  and  substituting  0.833  for  A,  and  M 
for  W,  we  have  (10.5  x  .833  x  6.66)M  =  58.J  M,  to  re 
present  the  material  required  in  al ;  —  the  same  as  in 
case  of  Fig.  47. 

The  uprights  of  the  Finck  truss  obviously  sustain 
12W,  namely,  3|  at  each  end,  3  in  the  middle,  and  1 
at  each  of  the  quarterings,  r  and  n.  But,  in  comparing 
this  with  the  Boll  man  truss,  it  seems  fair  to  offset  6  up 
rights,  not  including  the  end  and  centre  ones,  in  the 
Finck,  against  7  in  the  Bollman  truss  not  estimated  ; 
bus  leaving  10M  for  uprights  in  the  former,  making 


246  BRIDGE  BUILDING. 

a  total  of  68 JM,  for  compression  material,   excepting 
the  6  intermediate  uprights,  excluded  as  above. 

Both  of  the  above  considered  trusses  exhibit  a  beau 
tiful  simplicity,  and  facility  of  comprehension  in  prin 
ciple,  and  they  will  be  left  for  the  present,  for  a 
discussion  of  the 

POST  TRUSS. 

CXXXIY.  This,  like  the  two  preceding  plans,  is 
designated  by  the  name  of  its  distinguished  designer 
and  publisher,  S.  S.  Post,  Esqr.,  of  Jersey  City. 

Fig.  49  gives  a  general  view  of  the  only  specimen 
of  this  truss  which  the  author  has  had  an  opportunity 
of  examining.  It  is  a  sort  of  compromise  between  the 
trusses  represented  by  Figs.  18  and  19,  of  which  the 
object  sought  appears  to  have  been,  to  obtain  a  nearer 
approximation  to  the  most  economical  angle  of  incli 
nation  for  both  thrust  and  tension  members  (between 
chord  and  chord),  by  inclining  the  latter  at  an  angle 
of  45°,  and  the  former  at  a  less  angle  with  the  vertical. 
These  are  both  favorable  conditions,  considered  alone 
and  by  themselves,  as  we  have  already  seen  [LXV  and 
LXVI]  ;  and  it  is  proposed  to  compare  the  economy  of 
this  particular  arrangement,  with  that  of  a  truss  having 
vertical  posts,  with  oblique  tension  diagonals ;  as  well 
as  with  other  plans,  preceding  and  succeeding. 

Assuming  the  same  length  and  depth  of  truss,  and 
the  same  load,  both  constant  aud  variable,  as  in  the 
preceding  cases,  acting  at  the  points  x,  y,  w,  &c.,  let  w 
represent  the  greatest  variable  load  for  the  length  of 
one  panel,  and  w'  the  weight  of  superstructure  bearing 
upon  one  truss,  for  the  same  length,  supposed  to  be 
concentrated  at  the  nodes  of  the  lower  chord,  and  as 
sumed  to  be  equal  to  %w.  Also,  let  1  equal  the  verti 


COMPARISON  OF  PLANS.  247 

cal  depth  of  truss  (between  centres  of  chords),  and  let 
tension  diagonals  incline  45°,  and  posts  lean  1  horizon 
tally  to  3  vertically ;  the  space  between  posts  being 
two-thirds  of  the  depth  of  truss. 

FIG.  49. 

Mr.  PosCs  Truss 
a       5       e       d      e     f      g      h      i      Tc I 


n  m 


Then,  omitting  counter  ties  up  to  (/",  from  the  left, 
as  neutralized  by  weight  of  structure  ;  we  see  that  the 
weight  at  z,  being  only  j  as  great  as  at  the  other  nodes, 
on  account  of  the  short  space  xy,  3w  -r-  80  (or  3w", 
substituting  for  the  occasion,  w"  for  w  -f-  80),  represents 
the  proportionate  part  of  that  weight,  tending  to  ber.r 
upon  the  abutment  at  m ;  and  this,  with  VLw"  for 
weight  at  v,  and  20^tf"  for  weight  at  u,  +  "2$iv"  lor 
weight  at  t,  makes  63w"  accumulated  upon  if,  when 
#,  v,  u  and  t  alone  are  loaded. 

Now,  the  action  upon  this  truss  is  less  certain  and 
determinate  than  where  the  thrust  pieces  are  vertical, 
or  inclined  equally  with  the  tension  pieces.  But  sup 
posing  that  the  weight  of  superstructure  at  s,  or  at  5 
and  r  together,  neutralizes,  or  reflects  back  a  part 
equal  to  w',  or  JSOtt/',  =  27w"  nearly,  of  this  6Zw",  we 
have  a  balance  of36JV,  as  the  maximum  weight  for  if. 

Then,   whether  this  63w/r*  which  must  go  to  the 

*This  full  amount  63w"  is  used  here;  for,  although  it  is  assumed 
that  only  5,  part  of  it  is  transmitted  through  tf,  the  balance  is  restored 
from  weight  of  structure  which  otherwise  would  pass  to  the  abutment 
aty. 


248  BRIDGE  BUILDING. 

abutment  #t  m,  in  virtue  of  the  loads  at  x,  i?,  u  and  /, 
is  transferred  through  fs  to  s^,  or  through/?'  to  rh ;  or 
whether  it  is  divided  equally  or  unequally  between  the 
two,  is  not  quite  obvious.  But  assuming,  as  what 
might  seem  probable,  that  it  is  transferred  in  equal 
portions  to  s^and  rh,  in  that  case,  sg  sustains  as  a  maxi 
mum,  3(3?0"  for  weight  at  s,  +  half  of  63w",  making  — 
say  67«?"  ;  supposing  that  sg  and  re  sustain  none  of  the 
weight  of  structure ;  which,  though  probably  not 
strictly  true,  will  not  materially  affect  the  result. 

Again,  (we  are  now  considering  the  nodes  at  the 
lower  chord  as  being  loaded  successively  from  left  to 
right),  the  weight  at  r  gives  44  w"  to  rh,  in  addition  to, 
say  32w"  tending  to  be  transmitted  from  tf,  and  w'9  or 
27w"  for  structure,  making  103*0". 

For  maximum  weight  on  iq,  there  is  due  to  movable 
weight  at  q,  5'2>v",  +  Qlio"  from  sg,  +  27w"  on  account 
of  weight  of  structure,  making  146*0";  while  pk  sus 
tains  (60  +  103  +  27)M>",  =  190a?",  and  ol  sustains  (68  + 
146+27)w"  =  241".  The  maximum  weight  upon  nl,  is 
made  up  of  that  of  pk  +  f  (10+10')  at  n,  =  270i0". 

Having  thus  determined  the  maximum  weights 
which  these  diagonals  are  respectively  required  to  sus 
tain,  disregarding  some  small  matters  of  uncertainty, 
of  little  practical  importance,  we  find  the  sum  of  these 
maxima,  for  the  6  pieces  parallel  with  ue  on  the  right, 
to  be  783*0",  =  9.7875*0.  Then,  multiplying  by  2  (the 
square  of  the  common  length,  ay  being  =  1),  and  sub 
stituting  M'  for  w  (  as  M  was  substituted  for  W  in  the 
preceding  cases),  wre  derive  19.575M'  =  material  re 
quired  for  the  6  pieces  in  question.  Add  to  the  last 
amount  3.7M'  for  the  steep  diagonal  nl  (being  the  square 
of 'length  by  weight  sustained,  and  w  changed  to  M'); 


COMPARISON  OF  PLANS.  249 

and  we  have  the  whole  material  for  tension  obliques 
in  the  half  truss  ;  which  doubled,  exhibits  for  that  class 
of.  members  in  the  whole  truss,  46.55M';  omitting  6 
counter  ties,  not  required  to  sustain  structure  or  load, 
and  the  value  of  which  will  be  considered  (in  general) 
hereafter  under  the  head  of  counter  bracing. 

The  short  section  mn  of  the  lower  chord,  has  no  de 
terminate  action.  The  section  no  has  a  tension  equal 
to  J  of  the  weight  acting  on  nl  and  kn,  under  a  full 
load  of  the  truss,  equal  to  J  the  weights  upon  r,  p  and 
7?,  fur  nl,  and  J  of  those  at  r  and  p  for  kn  ;  the  whole 
equal  to  J  x2J  (w+w')+%  x2  (?(;+</;'),  =  2.11  w. 

To  this,  the  diagonal  ol  adds  at  o,  2  (w  +  wr),  and  10 
adds  J(w-fw'),  making  5.22z0  •«  tension  of  op;  while 
a  like  addition  at  p,  for  the  action  of  pk  and  hp,  shows 
8.332(7  for  /N/.  Again,  ^'  adds  at  q,  w+w',  equal  to 
1.33u',  while  rh  contributes  a  like  amount  at  r ;  mak 
ing  for  qr  and  rs  respectively,  a  tension  of  9.66*0,  and 
ll//;,  restoring  neglected  fractions. 

It  is  probable  that  a  small  decussation  of  forces 
through  re  and  sg,  under  a  full  load  of  the  truss,  would 
modify  these  stresses  slightly,  but  not  so  as  to  produce 
a  material  difference  in  the  final  results  of  the  present 
discussion. 

Summing  up  the  stresses  thus  determined  for  differ 
ent  portion  of  the  lower  chord,  counting  like  strains 
upon  corresponding  sections,  and  deducing  the  re 
quired  material  (as  above  done  with  regard  to  dia 
gonals),  remembering  that  the  length  of  sections  equals 
§  of  unit}',  we  obtain  41. IM'  =  material  required  in 
lower  chord.  This  added  to  46.55M',  the  amount  above 
determined  for  obliques,  gives  tension  material  for  the 
whole  truss,  equals  to  87.65M'. 


250  BRIDGE  BUILDING. 

Now,  it  is  manifest  that  the  quantity  here  represented 
by  M',  has  the  same  ratio  to  that  denoted  by  M  in  the 
estimates  of  material  for  trusses  Fig.  47  and  Fig.  48,  as 
the  weight  w  in  the  former  case  has  to  the  weight  W 
in  the  latter.  But  W  was  used  to  express  J  of  the 
gross  load  of  the  truss,  while  w  represents  only  -fa  of 
the  variable,  assumed  to  be  equal  to  j  of  the  gross  load. 
Therefore  w  :  W  :  :  f  x^  :  \  ;  whence,  w  =  0.6W ; 
and  M'  =  .6M.  This  equivalent  substituted  in  the  ex 
pression  87.65M',  gives  52.59M  =  tension  material  for 
the  post  truss. 

The  maximum  weights  sustained  by  the  thrust 
braces,  equal  respectively  those  borne  by  the  tension 
rods  communicating  such  weights,  and  for  the  5  pieces 
on  either  side  of  the  centre,  the  amount  is  equal  to  w" 
X  (36  +  67  -f  103  +  146+  190)  =  6.77w,  which  doubled, 
gives  13.54w;  for  the  whole  of  that  class  of  members. 
This  aggregate  weight,  multiplied  by  the  square  of  the 
common  length  of  pieces  (1.11),  with  w  changed  to  M' 
produces  15.02M',  =  9.01M. 

The  end  section  (kl)  of  the  upper  chord,  sustains 
compression  equal  to  the  weight  upon  ol  and  J  of  that 
upon  nl,  under  a  full  load  of  the  truss,  =  2  (10 -f  i#'), 
+  }x2f  (w+wf),  =  3.88w.  Add  2  (w+wf)  for  weight 
on  j9/c,  and  J  of  that  amount  for  that  on  ATI,  and  it 
makes  a  compression  of  7.44?#  upon  ki. 

Again,  adding  w+wf  ( =  1.33itf)  for  action  of  qi,  and 
J  of  the  same  for  that  of  io,  makes  9.22w  for  compres 
sion  of  ih,  while  a  like  addition  for  action  of  rh  and  hp, 
makes  10.99^  =  compression  of  hg  and  gf.  We  may 
call  the  last  stress  llw,  as  some  fractions  have  been 
neglected. 

The  above  amounts  of  stress  upon  the  several  sec 
tions  of  the  half  chord,  added  together  and  doubled  to 


COMPARISON  OF  PLANS.  251 

represent  the  whole  chord,  and  multiplied  by  the  length 
of  section  (f ),  produce  56.72w?,=  34.03  W  ;  whence, 
material  for  top  chord  =  34M  ;  very  nearly. 

The  two  end  posts  obviously  sustain  the  gross  load 
of  the  truss  (deducting  what  comes  upon  one  half  of 
the  short  spaces  mn  and  xy),  which  equals  9J  (w  -f 
wf),  =»  12.66w;  and,  the  length  being  1,  the  material 
equals  12.66M'  =  7.6  M. 

Summing  up  the  amounts  thus  determined,  of  mate 
rial  for  the  several  classes  of  thrust  pieces,  we  have : 

For  Braces,  or  inclined  posts, 9.01M. 

"    Upper  Chord, 34.00M. 

"    End  Posts, 7.60M. 

Total,  for  Thrust, ; 50.61M. 

"      "     Tension, 52.58M. 

WHIPPLE'S  TRAPEZOIDAL  TRUSS. 

CXXXV.  The  distinctive  characteristics  of  this  plan 
are,  an  Upper  Chord  made  shorter  than  the  Lower, 
by  the  width  of  one  panel  at  each  end,  giving  to  the 
truss  a  Trapezoidal  form  —  dispensing  with  non- 
essential  members,  and  proportioning  the  several  parts 
in  strict  accordance  with  the  maximum  stresses  to 
which  they  are  respectively  liable ;  principles  and  de 
vices  first  promulgated  in  the  original  edition  of  this 
work,  and  applied  by  its  author  in  the  construction  of 
trusses  with  parallel  chords,  with  or  without  vertical 
members. 

Truss  Fig.  50  has  vertical  posts  and  tension  dia 
gonals;  and,  using  w  and  w1  to  denote  the  same  quan 
tities  as  in  the  last  preceding  case,  and  pursuing  the 
method  explained  with  reference  to  Fig.  18,  [LVI],  we 
have  the  maximum  load  for  3/5  equal  to  4ivff  —  JM?' 


252 


BRIDGE  BUILDING. 


(malting  w"  «  w  divided  by  the  number  of  panels  = 
O.litf),  =  Aw —  £10,  since  w'  =  %w.  For  4/6,  we  have 
.610,  without  increase  or  diminution  on  account  of 
structure  ;  while,  for  the  3  next  diagonals  on  the  right, 
we  have  successively,. 9?0  +  JM/,  1.2*0  -f  w'  and  1.6i/;  + 
Ijz0',  making  altogether  3.7*0  +  3*0',  =  4.7z0  ;  showing 
for  the  5  pieces,  5.53w.  This  being  doubled  and  mul 
tiplied  by  square  of  length  (2.775),  and  w  changed  to 
M',  gives  material  for  10  long  diagonals  =  30.69M7. 


The  two  steep  diagonals  togther,  sustain  4  (w  -f 
w'),  =  5Jw,  which,  multiplied  by  square  of  length 
(1.44),  produces  material  =  7.68M';  while  the  two  ten 
sion  uprights  manifestly  require  2f  M'.  We  have  con 
sequently,  material  for  the  system  of  tension  obliques 
and  verticals  =  41.03m'. 

The  end  brace  obviously  sustains  4J  (w  +  w'),  and 
exerts  a  horizontal  stress  =  4?0  (two-thirds  of  the  weight 
borne),  upon  the  two  first  sections  of  the  lower  chord. 
The  steep  tension  oblique  adds  §  of  weight  borne,  mak 
ing  5.76^  for  the  next  section,  while  the  two  succeed 
ing  diagonals  toward  the  centre,  adding  1J  times  the 
weights  borne  successively  (under  a  full  load  of  the 
truss,  of  course),  give  8.42*0  and  10.19*0,  for  tension  of 
second  and  first  sections  from  centre,  respectively. 
Then,  adding,  doubling,  and  multiplying  by  length  of 
section,  we  obtain,  material  for  lower  chord  =  43.16M'. 


COMPARISON  OF  PLANS.  253 

Add  to  this  the  amount  for  diagonal  system  as  above 
found,  and  we  have  the  whole  amount  of  tension  ma 
terial  for  the  truss  =  84.18M'  =  50.5M. 

The  maximum  weights  sustained  by  obliques,  and 
by  them  transferred  to  7  thrust  verticals,  being  in  the 
aggregate  =  6.62*0,  the  length  of  members  being  unity, 
need  only  the  substitution  of  M',  to  express  the  re 
quired  material  for  said  verticals ;  which,  reduced  to 
terms  of  M,  equals  3.97M. 

The  first  and  second  sections  of  the  upper  chord,  ob 
viously  sustain  the  same  action  respectively,  as  the 
fourth  and  fifth  of  the  lower  chord  while  the  4  middle 
sections  of  the  former,  receive  the  additional  action  of 
diagonals  3\5/7  (upper  figures),  under  full  load. 
Hence  we  cipher  up,  material  for  upper  chord  =  32.6M. 

The  end  braces,  sustaining  9  (iv+ wf)  =»  12io,  with  a 
length  whose  square  is  1.44,  obviously  require  material 
=  (12xl.44)M'  =  10.37M. 

The  truss,  then,  requires  thrust  material,  for  upper 
chord,  32. 6M,  for  end  braces,  10.37M,  and  for  up 
rights,  3.97M  ;  making  a  total  for  the  truss,  of  46.09M. 

Tension  material  as  above,  total  50.50M. 

TRUSS  WITHOUT  VERTICALS. 

CXXXVI.  Assuming  a  truss  (Fig.  51),  of  same 
length,  depth,  and  number  of  panels,  and  same  load, 
variable  and  constant,  as  in  the  two  cases  last  consi 
dered,  with  diagonals  crossing  one  panel  only,  we  have 
nearly  the  Isometric  Truss,*  adopted  by  Messrs.  Steele 

and  McDonald. 

Arranging  the  numbers  over  the  diagram,  as  in  Fig. 
51,  and  using  the  process  explained  [XLVII,  Fig.  19],  it 

*  In  the  Isometric,  the  diagonals  incline  at  30°,  while  in  Fig.  51  they 
incline  nearly  o4°. 


254 


BRIDGE  BUILDING. 


will  be  seen  that  either  end  brace,  and  the  obliques 
parallel  therewith,  are  liable  to  maximum  weights  as 
follows,  proceding  from  end  to  end. 

FIG.  51. 


End  Brace    4.5  (w+  wr) 
Oblique^o.  1  ..................  2.100" 

"  "    2  ..................  1.533" 

"  "    3  .................  .  1.066" 

"  "    4  ..................  1.600" 

«  "    5  .....  .  .............  233" 

"  "    6  ., 


Compression.    Tension. 
6.000  w. 


.233?0 

.600  " 
1.066" 
1.533  " 
2.100  " 

2.666" 


Totals 


11.533i0 


Then,  doubling  for  the  two  sets,  multiplying  by 
square  of  length  (1.44),  and  changing  w  to  M',  we  have, 
to  represent  material.... for  compression  33.215M,  ten 
sion  23.616M'. 

The  end  brace,  sustaining  4.5  (w  -f-  w'}-,  =  6?tf,  exerts 
a  tension  of  4w  upon  the  end  section  of  the  lower 
chord.  The  next  brace  sustains  1£  (w  -f  wf)  =  2*0, 
making  a  tension  of  5.333z#  for  the  second  section. 
The  tension  and  thrust  diagonals  meeting  the  chord 

f  The  small  thrust  action  which  the  movable  load  tends  to  throw 
upon  6,  7  and  8,  and  the  small  tension  upon  1  and  2,  are  neutralized  by 
weight  of  structure. 


COMPARISON  OF  PLANS.  255 

at  the  next  node,  sustain  together  (under  a  full  load  of 
the  truss).  3  (w  -f  w'  =  4*0,  adding  -f  of  which,  gives 
Sw  =H  tension  of  the  3d  section,  while  2f?0  borne  by 
the  obliques  meeting  at  the  next  node,  makes  a  tension 
upon  the  4th  section  equal  to  9.777*0 ;  and  IJw;  at  the 
next  node  (the  tension  diagonal  only,  being  in  action, 
under  a  full  load),  gives  for  tension  of  the  5th  section, 
10.066*. 

Adding  the  stresses  of  the  several  sections  of  the  half- 
chord,  doubling,  multiplying  by  the  common  length 
(f),  and  changing  w  to  M'  shows  material  for  lower 
chord  =  50.37M,. 

The  end  section  of  the  upper  chord  sustains  thrust 
equal  to  f  x  (weight  on  end  brace,  (=  610),  -f  weight 
on  tension  oblique  meeting  said  brace),  =  f  8.66610  = 
5.77*0. 

The  two  obliques  meeting  at  the  first  node  from  the 
end,  sustain  together  4i0,  adding  2. 66610  to  the  above, 
and  making  a  compression  of  8.44  Iw  upon  the  second 
section  ;  while  succeeding  diagonals  make  the  stresses 
of  the  3d  and  4th  sections,  10.222*0,  and  ll.lw;  re 
spectively;  whence,  by  process  already  employed  and 
described,  we  derive : 

Material  for  upper  chord  — 47.392M'  =  28.435M 

Add  for  end  braces, 17.28  "   =  10.368" 

"     "    other  obliques, 15.935"  =    9.561" 


Total  for  compression  material,       80.607M'  =  48.364M 

Tension,  chord, 50.37M* 

Obliques, 20.616 

Verticals, 5 

78.986M'-47.391M. 

Grand  Total,  95.755M. 


256  BRIDGE  BUILDING. 


THE  ARCH  TRUSS. 

CXXXVTI.  A  parabolic  Arch  Truss  of  the  same 
length,  depth  and  load  as  allowed  in  the  five  preceding 
cases,  and  having  9  panels,  will  compare,  as  to  repre 
sentative  of  amount  of  material,  as  follows  : 

Let  w/  represent  the  variable,  and  wtn  =  \wt,  the  per 
manent  panel-lo*ad.  Then,  taking  the  greatest  depth 
of  truss  (15/.),  as  the  unit  of  length,  as  before,  the 
length  of  chord  will  be  6.666,  and  the  verticals  respect 
ively  1,  0.9,  0.7,  and  0.4. 

The  length  of  panel  (ll.lll/.),  being  divided  by  15/. 
(the  unit),  gives  0  .74074.  Hence,  tension  of  chord  = 

4  (w/  +  w/f)  x  '74t074,  =  1J  x  7.407410,,  which,  multiplied 

by  length  of  chord  (=  6.666),  and  wn  changed  to  M,, 
gives  representative  of  material  =  9.8765  x  6JM,  = 
65.843M, ;  in  which  M,is  the  unit  of  material,  proportional 
to  the  unit  of  length  (15',)  X  unit  of  stress,  wr 

The  maximum  tension  of  diagonals,  as  determined 
instrumentally  by  process  explained  [xxvn,  &c.,]  va 
ries  from  1.11  z^,  to  1 J^ ;  and,  taking  the  highest,  mul 
tiplying  by  the  aggregate  length  (15.4),  and  changing 
w,  to  M,,  we  obtain  material  =  20.52My. 

The  verticals  sustain  tension,  each,  =  lJw/5  with  an 
aggregate  length  of  6,  giving  material  =  SM,  ;  making 
a  total  of  tension  material  =  94.376M,. 

The  horizontal  thrust  of  the  arch,  must  be  in  all 
parts  the  same  as  the  tension  of  the  chord  (at  the  maxi 
mum  under  full  load),  and  it  is  manifest  that  the  ma 
terial  for  each  segment,  must  be  to  that  of  the  middle 
segment,  as  the  squares  of  respective  lengths  to  unity  ; 
that  is,  equal  to  material  in  said  middle  segment,  mul 
tiplied  by  squares  of  respective  lengths. 


COMPARISON  OF  PLANS. 


257 


But  the  representative  for  the  middle  piece  equals  Jth 
that  of  the  lower  chord,  =  7.31^,.  Hence,  this  amount 
multiplied  by  the  sum  of  squares  of  all  the  others,  +1 
for  the  middle  segment,  found  to  be  9.058  +  1,  =  10.058? 
gives,  to  represent  material  for  the  whole  arch,  73.584M/. 

Then,  the  vertical  members  are  liable  to  be  exposed 
to  compressive  action,  represented  by  the  small  amount 
of  2.058M,,  which  added  to  the  above^  gives  a  total  of 
compression  material,  equal  to  75. 642  M,. 

Now,  the  factor  My,  here  used,  is  to  the  factor  M 
used  in  the  preceding  cases,  manifestly,  as  fxj,  to  J, 
as  -Jj :  J,  whence,  12M/  =  8M  ;  and  we  reduce  the  co 
efficients  of  M,,  by  J,  and  change  M,  to  M,  to  bring  the 
last  results  to  the  same  standard  measure  as  in  the 
preceding. 

Effecting  these  changes,  we  have,  for  tension 
material,  Chord  43.895M,  -f»  Diagonals  13.689M  + 
Verticals  5. 333M,  equal  to  a  total  ol'62.917M.  For  com 
pression,  Arch,  49.056-r-Verticals,  1.372,  =  50.428M. 

•SYNOPSIS  OF  PRECEDING  DEDUCTIONS. 
The  following  tabulated  statement  may  promote  the 
convenience  of  comparison  : 


Trusses. 

Material  required  expressed  in  Ms. 

Designated. 

Tension 
total. 

Compression. 

Comp. 
Total. 

Grand 
Total. 

Chord. 

Ends. 

Posts,  &c. 

Bollman,  . 
Finck,  

05.296 
70.206 
52.590 
50.500 
47.391 
62.917 

58.333 
58.333 
34. 
32.6 
28.435 
{49.056 

7.000 
7. 
7.6 
10.37 
10.368 

* 

3.000 
9.01 
3.97 
19.561 
1.372 

65.333 
68.333 
50.610 
46.94 
48.364 
50.428 

130.629 
138.629 
103.200 
97.44 
95.755 
113.345 

Post,  
Whipple,  . 
Isometric,  . 
Arch,  

{Arch. 

33 


258  BRIDGE  BUILDING. 

CXXXVIII.  The  figures  in   this  table  are   to   be 
understood  in  all  cases  as  prefixed  to  the  quantity  M, 
which,  as  far  as  relates  to  tension  material,  represents 
a  determinate  amount  of  wrought  iron  ;  while,  as  it  re 
lates  to  compression  material,  M  represents  an  amount 
of  cast  or  wr-.-uy'-t  iron,  varying  as  the  forms  and  pro 
portions  of  parts  vary.     But,  in  the  present  discussion 
M  may  be  assumed  to  have  a  uniform  value  in  ex 
pressions  relating  to   material  under  the  heading  of 
chords;  and  of  ends,  whether  oblique  or  vertical. 

The  quantities  under  the  head  posts,  require  in 
general,  probable  twice  as  high  a  value  for  M,  as  tha.t 
required  for  the  other  classes  of  thrust  members,  as  it 
regards  all  but  the  first  named  truss,  while  the  first  is 
not  represented  in  that  column  at  all,  although  the 
parts  there  referred  to  are  as  indispensiblc,  practically, 
and  require  nearly  as  rrmch  material  as  corresponding 
parts  in  the  other  plans. 

With  regard  to  plan  No  2  (the  Finck),  6  posts  ac 
tually  required  (two  of  which,  at  the  quarterings,  sus 
tain  determinate  weight  equal  to  W  each),  are  also 
omitted  in  the  table,  to  place  this  plan  upon  an  equal 
footing  with  the  preceding  one. 

There  is  also  a  consideration  with  regard  to  the  ef 
fects  of  load  upon  these  two  trusses,  especially  the 
first,  which  render  it  partially  necessary  to  use  diagonal 
ties,  or  "  panel  rods"  in  the  several  panels  ;  and  such 
have  usually  been  introduced  wherever  such  bridges 
have  been  constructed. 

As  any  one  pair  of  suspension  rods  in  the  Boll  man 
truss  may  be  under  full  load,  while  the  others  are 
without  load,  the  loaded  node  would,  in  such  case,  be 
depressed,  while  that  on  either  side  would  retain  nearly 
its  normal  position.  Thus  would  result  an  obliquity 


COMPARISON  OF  PLANS.  259 

in  panels  adjacent  to  the  loaded  point,  and  consequently, 
a  tendency  to  kink  in  the  upper  chord,  by  opening 
the  joint  above  the  loaded  point  upon  the  under  side, 
and  the  next  joint  either  way,  upon  the  upper  side. 
Hence  the  compression  of  certain  chord  segments 
would  be  thrown  upon  the  extreme  upper  side  at  one 
end,  and  the  lower  side  at  the  other  end.  This  would 
be  decidedly  an  unfavorable  condition,  which  the  panel 
rods  are  used  to  obviate  by  distributing  the  load  of 
loaded  points  over  adjacent,  and  more  remote  parts  of 
the  truss.  Otherwise,  the  bridge  would  act  under  a 
passing  load,  somewhat  in  the  manner  of  a  pontoon 
bridge. 

By  estimating  a  reasonable  amount  of  material  for 
posts  and  panel  ties,  the  figures  in  the  table,  opposite 
the  first  two  trusses  would  be  materially  increased. 

Hence,  it  must  be  obvious  that  the  necessary  mate 
rial  for  the  two  above  named  trusses,  is  not  so  fully 
represented  in  the  table,  as  in  the  case  of  the  other 
four;  with  regard  to  which  —  assigning  proper  values 
to  M  in  the  different  columns  of  the  table,  and  assum 
ing  the  members  to  adhere  to  one  another  as  firmly  as 
the  different  portions  of  each  cohere  among  themselves, 
a  complete  truss  would  be  formed  in  either  case  (of 
dimensions  as  above  assumed),  sufficient  to  be  used  in 
a  bridge  required  to  bear  a  gross  load  equal  to  4  times 
the  weight  of  superstructure ;  provided  the  proper 
ratio  of  safe  variable  load  to  weight  of  structure  be  as 
3  to  1 ;  as  is  nearly  the  case  with  regard  to  a  100  foot 
bridge.* 


*  M,  in  the  preceding  table,  represents  a  piece  of  iron,  15'  long  sus- 
ficient  to  sustain  with  safety,  a  weight  W,  equal  to  ^  of  the  gross 
maximum  load  f>r  one  truss  of  a  100ft.  bridge.  Allowing  l,0091bs.  to 
the  linea!  foot  for  movable,  and  3331bs.  for  permanent  lo  -d,  W,  repre 
sents  -I  X  133,3331bs.=  16,66Glbs.  Then,  reckoning  the  safe  stress  of 


260  BRIDGE  BUILDING. 

In  such  case,  the  results  already  obtained,  would 
show  the  relative  cost  of  the  several  trusses  (excepting 
the  first  two),  with  almost  absolute  exactness. 

But,  as  the  parts  of  a  truss  can  not  be  so  connected 
and  welded  into  a  single  piece,  without  enlargements 
at  the  joinings,  by  any  skill  or  process  now  in  use,  we 
have  to  include  as  an  item  of  cost,  in  all  plans,  a  con 
siderable  amount  of  material  above  and  beyond  the 
net  lengths  and  cross-sections,  as  here  before  deter 
mined  with  regard  to  the  trusses  under  discussion,  re 
quired  for  the  lapping  of  parts,  screws  and  nuts,  eyes 
and  pins,  &c.,  to  form  the  connections  of  the  different 
members  with  one  another. 

With  regard  to  the  trusses  under  comparison,  no 
obvious  reason  presents  itself,  why  any  one  should  re 
quire  a  percentage  of  allowance  for  connections  ma 
terially  greater  than  another.  Leaving  out  the  two 
first,  as  perhaps  already  sufficiently  discussed,  the 
others  consist  of  about  the  same  number  of  necessary 
members,  and  with  the  exception  of  the  arch  truss,  ad 
mit  of  nearly  the  same  forms  and  connections  of  parts. 
The  Isometric,  or  Trapezoid  without  verticals,  presents 
the  fewest  lines  in  the  diagram;  but  some  six  of  those 
lines  represent  both  tension  and  thrust  members,  either 
separate  or  combined,  which  probably  complicates  the 

iron  (thrust  or  tension),  at  —  say  10,0001bs.  to  the  inch  of  cross-section, 
it  takes  If  square  inches  to  sustain  the  weight  W  ;  being  about  5£lbs. 
to  the  foot,  or  84flbs.  for  15'.  This,  increased  by —  say,  20  per  c.  for 
extra  material  in  connections,  gives  the  practical  value  of  M  ;  which, 
multiplied  by  the  co-efficient  of  M  in  the  table,  produces  approxi 
mately,  the  respective  weights  of  trusses. 

Now,  1£  X  84.37  ==  lOlilbs.  which  multiplied  by  113.345,  the  co 
efficient  for  the  Arch  truss,  gives  for  the  weight  of  that  truss,  11.4761bs. 
Add  for  10  feet  width  of  platform  (with  wooden  beams),  —  say  5,000ft. 
&.  m.  of  timber  and  plank,  equal  to  about  20,000  Ibs.,  and  we  have 
31.47Glbs.  to  represent  the  permanent  load  of  the  truss.  But  we  have 
assumed  a  truss  proportioned  to  sustain  with  safety  133,3331b.,  which 
is  a  little  more  than  4  times  the  weight  of  structure  here  above  esti 
mated  as  supported  by  the  truss. 


COMPARISON  OF  PLANS.  261 

details  of  connection,  quite  as  much  as  the  extra  three 
members  in  truss  No.  4.  The  Post  truss  presents  the 
larger  number  of  acting  members,  even  omitting  six 
counter  ties  seen  in  the  diagram,  with  apparently  no 
advantage  as  to  modes  of  connection.  Both  the  Post 
and  the  Isometric  have  10  members  represented  in  the 
4th  column  of  the  table,  whereas  the  Whipple  truss 
has  only  7,  and  these  the  shortest  of  all ;  and,  as  the 
material  in  these  parts  manifestly  acts  at  a  disadvan 
tage,  they  being  comparatively  long  and  slim,  and  sus 
taining  slight  action,  any  excess  in  their  number,  would 
seem  to  be  unfavorable  to  economy. 

It  is  believed,  however,  that  the  Post  truss  would  be 
improved  in  economy  by  reducing  it  to  a  trapezoidal 
contour,  as,  for  instance,  by  removing  the  parts  outside 
of  bx  and  kn  (Fig.  49),  and  changing  the  tension  pieces 
av  and  ol  for  others  connecting  6  with  y,  and  o  with  k ; 
thus  converting  the  figure  to  a  trapezoid  very  similar 
to  that  of  Fig.  50  ;  and,  by  striking  out  one  panel  from 
the  latter,  and  arranging  parts  as  in  Fig.  20,  except  as 
to  inclination,  the  relative  merits  of  inclined  and  ver 
tical  posts,  as  represented  in  these  two  plans  may  be 
fairly  tested. 

Analysis  of  trusses  modified  as  just  indicated,  show 
tension  material  slightly  in  preponderance  with  the 
vertical,  and  thrust  material  a  little  the  greater  with 
inclined  posts ;  the  average  being  about  one  per  cent 
greater  in  the  case  of  vertical  posts. 

This  balance,  though  trifling  in  amount,  is  upon  tho 
side  where  it  was  to  be  lookod  for,  in  view  of  the  re 
sult  of  investigations  had  with  reference  to  Figures  12 
and  13  [xxxix — XLVI],  as  well  as  the  case  of  the  Iso 
metric.  Both  the  Post  truss  and  the  Isometric,  as  to 
principle  of  action,  may  be  classed  with  Fig.  13,  where 


262  BRIDGE  BUILDING. 

weight  is  transferred  from  oblique  to  oblique,  and  not 
from  oblique  to  vertical,  and  the  contrary.  The  same 
may  be  said  of  truss  Fig.  15,  sometimes  called  the 
Triangular,  in  which  verticals  are  used  merely  to  trans 
fer  the  action  of  weight  from  the  point  of  application 
to  the  connections  of  the  obliques ;  after  which,  the 
weight  has  no  action  upon  verticals. 

Now  finally,  we  see  by  table  of  results,  that  if  the 
Post  truss  be  changed  to  the  trapezoidal  form,  as  above 
suggested,  it  will  occupy  a  position,  as  to  amount  of 
material,  or  more  strictly  speaking,  the  amount  of  ac. 
tion  upon  material,  between  Fig.  50  and  Fig.  51 ;  which 
latter  differ  from  one  another  less  than  2  per  cent ;  a 
difference,  which  would  undoubtedly  be  increased 
somewhat,  under  different  general  proportions  of  trusses. 
For  instance,  while  Fig.  50,  shows  an  inclination  of 
diagonals  used  in  connection  with  verticals,  probably 
nearly  approaching  the  optimum,  Fig.  51,  though  su 
perior  to  the  true  Isometric  (with  angles  of  60°),  in 
the  greater  inclination  of  its  obliques,  would  give  still 
better  results  with  an  inclination  of  about  40°. 

CXXXIX.  On  the  whole,  we  must  look  to  other 
quarters  than  the  amount  of  action  upon  material,  for 
plausible  ground  upon  which  to  found  a  decided  pre 
ference  for  either  of  the  three  plans  in  question.  A 
difference  of  two  or  three  per  C.,  and  even  more,  may 
easily  result  from  greater  or  less  facility  of  constructing 
and  erecting  the  structure,  while  a  regard  for  appear 
ance  may  also  be  worthy  of  consideration.  Hence, 
Engineers  and  builders  will  adopt  one  or  another  plan, 
according  to  individual  taste  and  judgment,  and  tho 
one  who  carries  out  the  principles  of  either  system  with 


COUNTER  BRACING.  263 

the  greatest  skill,  and  the  best  materials  and  workman 
ship,  will  probably  produce  tbe  best  bridge. 

Judging  from  the  preceding  tabulated  statement, 
the  arch  truss  seems,  prima  facie,  to  labor  under  a 
somewhat  formidable  disadvantage  in  the  fact  that  it 
shows  an  amount  of  action  upon  material  10  or  15  per 
cent,  greater  than  the  three  preceding  plans  just  es 
pecially  referred  to.  But  for  the  light  of  experience, 
we  might  be  led  to  discard  the  plan  without  a  trial. 

But,  having  chanced  to  be  the  first  plan  of  iron 
Truss  successfully  put  in  use,  and  having  had  its  ca 
pabilities  fully  tried  and  demonstrated,  before  any 
formidable  competitor  appeared  in  the  field,  it  could  not 
be  dislodged  from  its  position,  until  a  rival  plan  could 
not  only  theoretically,  but  also  practically  demonstrate 
its  superior  claim  to  public  favor. 

The  result  has  been  such  as  to  show  that  even  a  very 
considerable  excess  of  action  upon  material,  may  be 
overbalanced  by  more  advantageous  action  of  thrust 
material,  and  greater  simplicity  and  facility  of  construct- 
tion  ;  insomuch  that  the  Whipple  Patent  Arch  Truss, 
with  trifling  modifications  from  the  original  pattern, 
has  competed  successfully  with  all  other  plans,  for  the 
class  of  structures  it  was  originally  designed  and  re 
commended  for  (common  bridges  of  50  to  100  feet), 
during  more  than  a  quarter  of  a  century,  which  has 
been  fruitful  in  efforts  at  improvement  in  iron  bridge 
construction. 


COUNTER  BRACING. 

The    elasticity   of   solid    materials,    is   manifested 
in  bridge  trusses,  by  their  downward  deflection  under 


264  BRIDGE  BUILDING. 

load,  and  the  recovery  of  their  previous  form  and  po 
sition  on  the  removal  of  the  load. 

Tins  arises  principally,  from  the  temporary  elonga 
tion  of  parts  exposed  to  tension,  and  the  contraction 
of  those  exposed  to  compression,  according  to  laws 
and  principles  supposed  to  be  understood. 

The  deflection  of  trusses  within  the  usual  limits, 
when  properly  proportioned,  is  not  essentially  detri 
mental  to  their  safety  and  durability ;  but  rather 
enables  them  the  better  to  resist  sudden  impulses, — 
except  in  case  of  a  regular  succession  of  impulses,  at 
intervals  corresponding  with  those  of  the  natural  vi 
brations  of  the  structure,  or  with  some  multiple  or 
even  division  thereof;  a  result  frequently  noticeable, 
and  sometimes,  to  a  degree  somewhat  unpleasant  to 
the  eye.  as  well  as  suggestive  of  danger.  Hence, 
great  emphasis  is  often  employed,  in  expressing  the  sup 
posed  advantages  of  "  counter  bracing,"  as  a  means 
of  stiffening  trusses,  and  preventing,  or  diminishing 
their  vibration. 

What  is  technically  called  "  counter-bracing,"  as  ap 
plied  to  bridge  trusses,  is  the  introduction  of  a  set  of 
diagonal,  or  oblique  pieces  or  members,  to  act  in  an 
tagonism  to  the  main  diagonals,  whether  acting  by 
tension  or  thrust,  which  contribute  toward  sustaining  the 
weight  of  structure  and  load;  the  object  being,  to  re 
tain  in  the  truss  when  unloaded,  more  or  less  of  the 
deflection  produced  by  the  load,  when  the  truss  is 
loaded. 

My  object  at  the  present  time  is,  to  exhibit  the  pro 
cess  and  results  of  my  investigations  as  to  the  theory 
and  effects  of  this  counter-bracing,  as  usually  practiced 
in  bridge  building,  and  to  state  the  conclusions  arrived 


COUNTER  BRACING. 


265 


at,  as  to  the  value  of  counter-braces,  towards  effecting 
the  object  proposed.  « 

FIG.  52. 
a b      c       d       e      f       fj       h  .    i 


I  assume  a  truss  (see  Fig.  52)  composed  of  horizon 
tal  chords  (of  equal  lengths),  at  top  and  bottom,  vertical 
posts,  and  diagonal  tension  rods,  inclined  at  45°,  or  at 
any  other  given  inclination, — the  truss  being  uni 
formly  loaded  from  end  to  end,  and  so  proportioned 
that  all  of  the  above  named  parts,  in  that  condition  of 
the  load,  shall  undergo  an  amount  of  extension  or 
compression,  proportional  to  the  respective  lengths  of 
pans,  multiplied  by  a  constant  factor  (E),  equal  to  the 
elastic  change  effected  in  a  length  equal  to  that  of  the 
uprights  between  centres  of  chords,  which  is  assumed  as 
the  unit  of  length  for  the  occasion.  Then,  let  L  repre 
sent  the  length  of  truss,  P,  the  number  of  panels,  ff, 
equal  to  L-r-  P,  the  horizontal  reach  of  diagonals,  and 
D  (equal  to  2LE),  the  difference  in  length,  occasioned 
by  extension  of  lower,  and  compression  of  upper  chord. 

Now,  assuming  no  change  in  lengths  of  diagonals 
and  verticals,  it  is  manifest  that  the  chords  assume,  in 
these  circumstances,  the  forms  of  two  similar  and  con 
centric  arcs  of  circles,  of  which  the  difference  in  length 
'is  to  the  mean  length,  as  the  difference  of  radii  is  to 
the  mean  radius,  R. 

But  the  difference  of  radii  manifestly  equals  the 
distance  between  chords,  equal  to  L  Using,  then, 
the  representative  signs  before  adopted,  we  have 

D  :  L  :  :  1  :  E;     whence  R  =  L-±D. 

34 


266 


BRIDGE  BUILDING. 


the  depression  at  the  centre  of  the  truss,  is 
evidently  equal  to  the  versed  sine  of  half  the  arc  made 
by  the  chords,  and  is  found  with  sufficient  nearness, 
by  the  equation  .  .  Dep.  =-  (±Lf  -v-  2R,  =  JZ,2  -r-  R. 
Then,  substituting  L  -s-  D  for  R,  we  have  dep.=  \U  -r- 
(Z,  -s-  D),  =  IDL. 

Hence,  if  the  length  of  truss  equal  8  times  the  depth, 
or  8,  the  deflection  due  to  this  cause,  will  equal  the 
difference  in  length  of  the  two  chords,  produced  by 
their  extension  and  compression. 

Again,  if  length  equal  6,  then,  dep.=  JD  x  6,  == 
3D  -T-  4,  =  9E. 

The  depression  resulting  from  extension  of  diagonals, 
may  be  illustrated  as  follows. 

If  the  points   a  and  b  of  a  rectangular  panel  abed 
(Fig.  53),  be  fixed,  and  ac  be  extended  by  an  addition 
FIG   53  equal  to  eh  to  its  length,  produced  by 

d  the  action  of  weight  at  c,  either  di- 
g  rectly,  or  through  the  upright  dc  ;  the 
points  d  and  c  will  fall  to  g  and  h, 
and  the  very  small  triangle  ceh  (eh 
representing  only  the  elastic  stretch 
of  ac),  will  be  essentially  similar  to  abc  ; 
whence,  ch  :  ac  :  :  eh  :  aby  and  eh  : 
ac  :  ab,  :  :  V  (1  +  H2)  :  1  .  .  .  Therefore,  eh  = 
(1  -f  H2).  But  ch  :  ^  (1  +  H2}  :  :  eh  :  1,  :  : 
(1  -f  H2)  :  1  ;  consequently,  .  .  ch  =  E  +  EH2. 
Now,  if  this  represent  one  of  the  end  panels  of  a 
truss,  all  parts  of  the  truss  between  the  end  panels, 
must  descend  through  a  space  equal  to  ch,  in  conse 
quence  of  the  extension  of  diagonals  in  the  two  end 
panels  ;  and  so  for  each  succeeding  pair  of  diagonals, 
to  the  centre  of  the  truss.  Therefore,  the  depression 


E 


COUNTER  BRACING.  2G7 

iu  the  centre,  due  to  the  stretching  of  diagonals,  must 
be  equal  to  JP  x  (1  +  H2)E,  =  (JP  +  }  PH2)E. 

The  depression  in  the  centre  of  the  truss,  due  to 
compression  of  uprights,  is  simply  equal  to  the  aggre 
gate  compression  of  all  the  uprights  on  either  side  of 
the  centre  one,  and  consequently,  equal  to  %PE.  This 
amount  added  to  that  produced  by  extension  of 
diagonals,  as  above  determined,  makes,  for  up 
rights  and  diagonals  together,  a  depression  equal  to 


The  value  of  this  last  expression,  length  and  depth 
of  truss  being  the  same,  varies  slightly  with  variation 
in  number  and  width  of  panels,  but  not  so  as  to  be  a 
matter  of  practical  importance. 

Assuming  L  =  8w,  =  8,  we  find  that, 

P  =  2,  and  P  =  16,  make  (P  +  J  PR  2)E  =  ISE. 

P=4,  andP  =    8       «  " 

P=6,  makes        " 

6  panels,  therefore,  seem  to  produce  the  least  deflec 
tion. 

The  deflection  resulting  from  changes  in  leng  hs  of 
chords,  has  been  shown  to  be  equal  to  \LD  ;  and, 
substituting  PHfor  L,  &  ZPHEior  D,  we  have.  .  J- 
LD—  JPJjfZ2j57,  =deflectiou  from  change  in  chords. 

The  term  E,  then,  with  the  following  co-efficients, 
expresses  the  depression  at  the  centre  of  the  truss,  re 
sulting  from  all  changes  in  length  of  parts,  namely, 
for  chords,  JP»JEP,  for  diagonals,  ......  JP+JPl?8,  and, 

for  uprights,  JP. 

Hence,  the  deflection  of  a  truss,  under  the  condi 
tions  here  assumed,  depends  upon  three  simple  ele 
ments,  represented  by  the  letters,  P,  H,  &  E;  and  is 
expressed  in  the  following  general  formula  ; 

Deflection^  (iP27P,  +  JP+  JPH2,  + 


268  BRIDGE  BUILDING. 

The  parts  of  this  aggregate  co-efficient  of  E,  re 
ferring  respectively  to  chords,  diagonals,  and  uprights, 
are  separated  and  distinguished  by  commas. 

The  formula  just  given  is  equally  applicable  in  case 
of  thrust  diagonals  and  tension  verticals ;  as  will  be 
made  obvious  by  a  moment's  examination  of  the 
principles  involved. 

Now,  if  the  truss  could  be  anchored  down,  by  ties 
and  anchorage  absolutely  unyielding,  to  the  point  of 
its  utmost  deflection  under  load ;  the  load  might  be 
removed,  and  replaced,  without  any  rising  or  falling 
of  the  truss, — the  load  and  the  anchors  alternately  re 
taining  the  deflection,  and  preserving  a  constant  and 
uniform  strain  upon  the  truss. 

The  same  effect  is  partially  produced  by  counter- 
bracing  ;  and  the  object  of  the  present  investigation  is, 
to  determine,  approximately,  at  least,  to  what  extent 
this  may  be  done,  and  what  is  the  real  advantage  of 
counter-braces,  in  trusses  with  parallel  chords  ;  beyond 
where  they  are  necessary,  to  counteract  the  effects  of 
unequal  variable  load,  upon  the  different  parts  of  the 
truss. 

We  have  seen  that  deflection  results  from  three 
causes,  all,  of  course,  depending  upon  elasticity ; 
namely  ;  difference  effected  in  lengths  of, — first  chords, 
second,  diagonals,  and  third,  uprights. 

The  theory  of  counter-bracing  is,  that  by  the  intro 
duction  of  antagonistic  diagonals,  the  material  is  pre 
vented  from  regaining  its  normal  state  on  removal  of 
the  load ;  and  consequently,  that  it  yields  to  the  re- 
imposition  of  load,  to  much  less  extent  than  it  would 
do,  in  the  absence  of  counters. 

As  to  the  deflection  due  to  the  difference  in  lengths 
of  chords,  equal,  as  shown  by  the  general  formula  one 


COUNTER  BRACING.  269 

page  back,  to  one-half  of  the  whole,  for  a  truss  in  which 
L  =  6/Z,  and  to  more  than  half,  when  L  is  greater 
than  611;  the  counter-diagonals  have  no  tendency  to 
retain  or  diminish  that  difference,  or  the  deflection 
produced  by  it.  The  diagonals  and  counters,  simply 
contract  or  extend  (according  as  they  act  by  tension  or 
thrust),  the  two  chords  equally,  without  affecting  the 
difference  between  the  two. 

On  the  contrary,  the  action  of  the  counter  diagonal 
tends  to  retain  the  tension  (or  thrust,  in  case  of  thrust 
diagonals),  of  the  main  in  the  same  panel,  and  also, 
the  compression  (or  tension),  of  uprights ;  and,  in  as 
far  as  that  is  accomplished,  the  deflection  due  to  the 
elasticity  of  those  parts,  is  retained,  on  removal  of  load 
from  the  truss. 

Suppose,  in  a  truss  with  tension  diagonals,  loaded 
and  depressed  as  already  explained,  and  all  parts  ex 
tended  or  contracted  to  the  amount  of  E  X  respective 
lengths ;  a  counter-diagonal  to  be  inserted  in  each 
panel,  crossing  the  mains,  as  shown  in  the  diagram 
(Fig.  52),  and  of  half  the  size  of  the  latter,  such  being 
the  usual  proportion  for  counters. 

Now,  the  counters  being  adjusted  so  as  not  to  act 
while  the  load  is  on,  but  ready  to  act  immediately,  as 
the  main  diagonals  begin  to  contract,  then,  the  load 
being  removed,  the  main  will  contract  by  its  elasticity, 
opposed  by  the  counter,  until  they  come  to  an  equili 
brium  ;  each  sustaining  the  same  amount  of  tension. 
Still,  the  aggregate  extension  of  the  two  beyond  the 
natural  state,  must  be  essentially  the  same  as  that  of 
the  one,  under  the  load;  the  one  gaining,  just  as  fast 
as  the  other  loses. 

But  the  main,  having  a  cross-section  twice  as  great 
as  the  counter  (chords  and  uprights  retaining  the  same 


270  BRIDGE  BUILDING. 

lengths),  must  lose  two-thirds  of  its  tension,  while  the 
latter  is  acquiring  strain  enough  to  withstand  the  re 
maining  third.  Hence,  2  thirds  of  the  deflection  due 
to  extension  of  diagonals,  is  recovered,  on  removal  of 
the  load,  while  the  counter-diagonal  retains  the  other 
1  third. 

But  the  posts  (the  greater  portion  of  them),  do  not 
remain  stationary  as  to  length,  as  above  assumed  ;  the 
main  and  counter  diagonals  together,  exerting,  ob 
viously,  only  f  as  much  action  upon  them  in  the  new 
condition,  as  the  former  exert  under  load,  they  are  re 
lieved  of  J  of  their  aggregate  stress  under  load ;  but 
do  not  recover  in  the  same  degree,  their  original  ag 
gregate  length ;  for  the  relief  falls  mostly  upon  the 
larger  uprights,  where  the  relative  effects  are  less  than 
the  average. 

To  illustrate  the  case  as  to  uprights — if  equal 
weights  act  at  the  nodes  of  the  lower  chord  (Fig.  52), 
the  compressive  action  upon  the  posts  at  p,  q,  r,  and  s, 
is  obviously  as  1,  3,  5,  7,  respectively,  or  as  3ft,  9ft, 
15??,  21rc.  [See  analysis  of  Fig.  12].  Then,— Counter- 
bracing,  and  removing  load ;  sa  is  relieved  of  two-thirds 
of  its  stress,  equal  to  14??,  while  bs  exerts  a  force  of  7n 
upon  br,  making  with  5??  retained  by  bq,  a  total  of  12ft 
upon  br,  and  showing  a  relief  of  3ft.  Again  ;  cq  receives 
5ft  through  cr,  and  3ft  through  cp,  =  8?i  in  all,  being  a 
relief  of  In.  But  dp,  receiving  3ft  through  dq,  and  In 
retained  by  do,  sustains  4n,  being  an  increase  of  In. 

Now,  as  these  uprights  are  assumed  to  undergo  the 
same  contraction  under  load,  J  of  the  deflection  on  ac 
count  uprights,  is  due  to  each.  Therefore,  sa  being 
relieved  of  2-3ds  of  its  action,  restores  .  .  2-3ds  of  J, 
(=  16.6  per  C.),  of  that  deflection.  In  like  manner,  br 
restores  l-5th  of  J,  =  5  per  C.,  and  cq  l-9th  of  J,  or  2.8 


COUNTER  BRACING.  271 

per  C.,  making,  for  the  pieces  together,  24.4  per  C.,  re 
stored.  This  is  diminished  by  l-3d  of  J,  or  8.3  per  C. 
(on  account  of  increased  compression  upon  c/p),  leaving 
a  balance  of  16.1  per  C.  only,  of  deflection  from  con 
traction  of  uprights,  which  is  restored  in  spite  of 
counter-diagonals,  in  the  case  under  discussion. 

Moreover,  the  main  and  counter  diagonals,  produc 
ing  more  or  less  effect  of  contraction  upon  the  chords, 
according  to  the  degree  of  inclination  of  the  former, 
and  the  cross-sections  of  the  latter,  it  may,  perhaps,  be 
reasonably  assumed,  that  the  contraction  thus  effected 
in  the  horizontal,  is  a  full  offset  to  the  16  per  C.  of  ex 
pansion  in  the  vertical  sides  of  panels,  as  above  shown; 
BO  that  we  may  regard  the  whole  deflection  from  up 
rights,  as  being  retained  by  counter-diagonals. 

To  state  the  full  result  of  the  foregoing  investigation 
then,  we  tind  in  case  of  Fig.  52,  which  is  a  fair  repre 
sentative  of  the  average  of  trusses;  that  counter-brac 
ing,  obviates  all  the  deflection  due  to  compression  of 
uprights,  together  with  J  of  that  resulting  from  exten 
sion  of  diagonals  ;  and,  making  H  =  1,  in  the  formula 
for  deflection  (p.  267),  we  have  —  deflection  saved  by 
counter-diagonals,  =  (J  X  8  -f  4)  -*-  28,  =  a  little  less 
than  24  per  C.  of  the  whole  deflection.  If  //==  0.75 
(truss  52),  the  result  would  be  about  31J  per  C.  saved. 

But  even  these  results  are  based  upon  condition^ 
never  occurring  in  practice.  It  has  been  assumed  that 
all  parts  of  the  truss  undergo  equal  degrees  of  change 
under  a  full  load  ;  which  may  be  nearly  true  with  re 
spect  to  chords,  but  not  to  other  parts.  The  maximum 
action  upon  od  and  dp  (Fig.  52),  requires  those  parts  to 
be  2J  times  as  great,  as  they  need  be  under  full  load  ; 
while  pc  and  cq  require  £  more,  and,  qb  and  6r,  l-20th  more 


272  BRIDGE  BUILDING. 

cross-section  at  the  maximum,  than  under  a  full  load 
of  the  truss. 

Now  the  deflection  resulting  from  elasticity  in  these 
parts,  being  less  in  proportion  as  the  parts  are  greater, 
the  saving  by  counter-bracing,  must  be  less  in  the  same 
degree,  as  far  as  it  relates  to  such  parts.  This  at  once 
reduces  the  above  computations  for  deflection  retained, 
from  31 J  and  24,  to  25  and  19  per  C.,  for  the  two  cases 
respectively ;  and,  considering  the  increase  of  section 
required  for  uprights  (in  iron  trusses),  on  account  of 
great  length  and  small  diameter,  as  heretofore  alluded 
to,  it  is  deemed  to  have  been  fully  demonstrated,  that 
the  effects  of  counter-diagonals,  of  half  the  size  of  the 
mains,  are,  to  retain  in  the  truss  when  unloaded,  from 
one-sixth  or  "less,  to  one-fourth  of  the  deflection  pro 
duced  by  a  full  movable  load. 

But  it  has  been  seen  in  the  progress  of  our  investi 
gations  as  to  the  action  of  load  upon  the  different  parts 
of  the  truss,  that  counter-diagonals  are  required  in  one 
or  two  panels  on  either  side  of  the  centre,  and  there, 
they  can  not  be  safely  omitted.  But,  beyond  the  point 
where  the  weight  of  structure  acting  on  the  mains,  be 
gins  to  overbalance  the  effects  of  unequal  and  variable 
load  upon  the  counters,  I  do  not  consider  the  advan 
tages  of  counter  diagonals  to  be  sufficient  to  warrant 
their  use. 

In  the  case  of  rail  road  trains,  gliding  smoothly  over 
bridges  of  ordinary  spans,  a  quarter  or  a  half  of  an 
inch  more  or  less  of  deflection,  is  of  slight  importance, 
while,  in  bridges  for  ordinary  carriage  travel,  the  only 
objection  to  it  is,  that  it  slightly  increases  the  degree 
of  vibration  produced  by  successive  impulses,  as  of  the 
trotting  of  animals,  in  time  with  the  natural  vibrations. 
Now,  counter-bracing  tends  to  shorten  the  intervals  of 


COUNTER  BRACING.  273 

the  natural  vibrations  by  diminishing  their  extent;  but 
can  not  destroy  the  liability  to  vibration  ;.and  the  al 
teration  of  interval  produced,  may  as  often  bring  the 
vibrations  nigher  in  tone  with  the  gait  of  a  trotting 
horse,  as  otherwise.  "In  certain  cases  the  effect  would 
be  one  way,  and  in  others,  the  opposite;  and  in 
general,  the  only  result  would  be,  to  diminish  the  ex 
tent  of  motion  ;  by  one  quarter,  or  less. 

Such  is  the  result  of  the  best  reasoning  and'science 
that  I  have  been  able  to  bring  to  bear  upon  the  subject 
of  counter-bracing. 

To  find  the  actual  maximum  deflection  of  a  truss  it 
is  only  necessary  to  know  the  value  of  P  and  //,  and 
to  assign  to  E  a  value  determined  by  the  character  of 
material,  and  the  stress  upon  the  several  parts  under 
full  load. 

In  Fig.  52,  if  II  =  1  =  12|ft.,  and  the  tension  of 
wrought  iron  equal  15,0001bs.  per  square  inch,  the 
value  of  E  for  that  material,  will  be  about  0.0075  ft. ; 
and  this  will  apply  to  the  lower  chord,  and  the  obliques, 
ar  and  li.  But  the  average  value  of  E'  for  diagonals 
of  wrought  iron,  would  be  about  0.006ft. 

For  cast  iron,  ll,0001bs.  to  the  square  inch,  requires 
about  the  same  value  for  E,  as  15,000  upon  wrought 
I. ;  and,  as  that  is  a  fair  working  rate  of  compression 
for  cast  iron  in  the  upper  chord,  .0075ft.  may  be  taken 
as  Ae  value  of  E  for  chords,  in  general.  Uprights, 
for  reasons  heretofore  explained,  require  a  value  for 
E',  not  greater  than  .005ft. 

The  above  values  of  E  and  H,  substituted  in  the 
formula  (J  P*H\  +  JP  +  JP#2,  +  JP,)  x  E,  it  becomes 
±P*H*E+  (JP  +  ±PH*}Ef  +  \PE»,  equal  to  J  x  64  x 
.0075,  +  (4  +  4)  .006,  +  4  x  .005,  =,  0.188ft.  =  about 
2J  inches.  Hence,  a  well  proportioned  wrought  and 
35 


274  BRIDGE  BUILDING. 

cast  iron  truss,  one  hundred  feet  long,  by  12J  feet  deep, 
may  be  depressed  2J"  in  the  centre  by  a  distributed 
load  (including  structure),  with  tension  not  exceeding 
15,  and  thrust,  not  exceeding  11  thousand  pounds  to 
the  square  inch  in  cross-section  of  iron. 


WOODED  BRIDGES. 

STRENGTH  OF  TIMBER,  &c. 

CXL.  The  qualities  of  wood  as  a  building  material, 
have  been  extensively  treated  of  by  authors  whose 
works  have  long  been  before  the  public,  with  a  degree 
of  ability  and  research  to  which  the  present  writer  can 
make  no  pretensions.  He  will  therefore  at  this  timof 
simply  state  the  conclusions  arrived  at  from  reading 
and  observation  (coupled  with  some  experimental  re 
search)  with  respect  to  the  average  absolute  strength, 
positive,  negative,  transverse,  and  to  resist  splitting,  in 
certain  cases ;  of  the  timbers  principally  in  use  for 
building  purposes;  as  also,  the  forces  they  will  bear 
with  safety  under  various  circumstances ;  leaving  it, 
of  course,  for  others  to  adopt  his  views  for  their  own 
practice,  or  to  modify  and  correct  them,  according  as 
their  greater  experience  or  better  judgment  may 
dictate. 

At  the  same  time,  the  author  may  be  allowed  to  ex 
press  his  firm  belief,  that  the  views  about  to  be  pre 
sented,  if  fairly  observed,  will  lead  to  the  adoption  or 
continuance  of  a  safe  and  economical  practice  as  to  the 
proportioning  of  timber  work  in  bridge  construction. 

Pine  timber  in  this  country  is  perhaps  to  be  ranked 
as  among  the  most  valuable  timber  in  use  for  building 
purposes ;  especially  in  bridge  building.  White  oak, 


WOODEN  BRIDGES.  275 

and  some  other  varieties,  are  preferred  for  certain  pur 
poses,  as  being  harder,  stiffer,  and  especially  better 
calculated  to  sustain  a  transverse  action,  whether 
tending  to  bend  or  crush  it.  But  in  what  follows, 
reference  will  principally  be  had  to  the  ordinary  white 
pine  of  this  country ;  and  the  deductions  here  made, 
may  readily  be  modified  so  as  to  apply  to  other  mate 
rials  of  known  strength,  when  so  required. 

The  absolute  positive,  or  tensile  strength  of  pine, 
may  be  stated  at  about  10,OOOJbs.  to  the  square  inch 
of  cross-section.  It  might  therefore  seem  to  be  safely 
reliable  in  practice,  at  15  or  16  hundred  pounds  to  the 
inch,  upon  that  part  of  the  section  of  which  the  fibres 
are  not  separated  in  forming  connections  with  other 
parts  of  the  structure.  And  so  it  probably  would  be, 
when  new,  sound,  and  straight  grained.  But  timber 
in  bridges,  is  usually  more  or  less  exposed  to  wetting 
and  drying,  and  deterioration  in  strength, —  especially 
as  it  regards  tension.  Moreover,  in  forming  connections 
of  parts  and  pieces  in  a  structure,  it  is  difficult  to  se 
cure  a  uniform  strain  upon  all  the  uncut  fibres; —  one 
side  of  the  piece  being  often  exposed  to  much  greater 
stress  than  the  other.  In  view  of  such  facts,  it  is 
deemed  advisable  to  seldom  allow  less  than  one  square 
inch  section  of  unbroken  fibre  to  each  l,0001bs.  of 
tensile  strain. 

NEGATIVE  STRENGTH  OF  TIMBER. 

CXLI.  The  ability  of  pine  to  resist  compression  in 
the  direction  of  the  length  of  piece,  is  from  4  to  5  thou 
sand  pounds  to  the  square  inch  of  section,  and  this 
varies  but  little,  whether  the  pieces  be  of  length  equal 
to  once,  or  five  or  six  times  the  diameter.  It  moreover 


276 


BRIDGE  BUILDING. 


diminishes  only  about  one-third  with  an  increase  of 
length  up  to  18  or  20  diameters. 

!N"ow,  if  we  take  about  |  of  the  absolute  strength, 
say  800ft>s.  to  the  inch  for  a  length  of  6  diameters,  and 
560  for  18  diameters,  and  substract  40ft>s.  per  inch  for 
every  increase  of  2  diameters  in  length,  between  6  and 
18  diameters;  and  from  18  to  40  diameters,  compute 
the  quantities  by  the  rule  given  [LXXXIX],  in  relation 
to  negative  resistance  of  cast  iron,  we  shall  form  a 
table  of  negative  resistances  of  timber,  for  a  range  of 
lengths  which  will  cover  the  principal  cases  that  will 
occur  in  bridge  building,  which  the  author  feels  confi 
dent  in  recommending  for  the  adoption  of  engineers 
and  practical  bridge  builders.  If  it  be  desired  to  ex 
tend  the  table  to  greater  lengths  than  40  diameters, 
the  formula  which  makes  the  strength  as  the  cube  of 
the  diameter  divided  by  the  square  of  the  length,  may 
properly  be  used. 

The  following  brief  table  of  negative  resistance  of 
timber,  has  been  constructed  in  the  manner  above  in- 

Table  of  Negative  Resistance  of  Timber. 


Diameters. 

Pounds. 

Diameters. 

Pounds. 

Diameters. 

Pounds. 

6 

800 

24 

368 

42 

166 

8 

760 

26 

328 

44 

151 

10 

720 

28 

296 

46 

138 

12 

C80 

30 

269 

48 

127 

14 

640 

32 

246 

50 

117 

16 

600 

34 

227 

52 

108 

18 

560 

36 

210 

54 

100 

20 

479 

38 

195 

57 

90 

22 

416 

40 

183 

60 

81 

dicated,  and  exhibits  at  a  single  view,  the  number  of 
pounds  to  the  square  inch  of  cross-section,  which  tim 
bers  of  different  lengths  will  bear  with  safety,  at  inter- 


WOODEN  BRIDGES.  277 

vals  of  2  diameters  in  length,  for  all  lengths  between  6 
and  60  diameters.  The  first  column  gives  lengths  in 
diameters,  and  the  second,  the  number  of  pounds  to 
the  square  inch,  borne,  with  safety. 

TRANSVERSE  STRENGTH  OF  WOOD. 

CXLII.  Pine  timber  will  bear  a  transverse  strain  of 
1500  or  1600flbs.  to  the  square  inch  of  cross-section  ; 
that  is,  the  projecting  end  of  a  beam  will  bear  1500Sbs. 
for  each  square  inch  of  its  cross-section,  applied  at  a 
distance  from  the  fulcrum  equal  to  the  depth  of  the 
beam  ;  the  force  acting  parallel  with  the  sides.  In 
other  words,  a  beam  1  inch  square  upon  supports  2 
inches  apart,  will  sustain  3,000ft>s.  midway  of  supports, 
provided  the  timber  be  not  split  or  crushed  ;  as  would 
certainly  be  the  case  with  so  short  a  leverage. 

It  will  therefore  be  proper  in  practice,  never  to  ex 
pose  this  material  to  a  greater  transverse  strain  than 
250Ibs.  (upon  a  leverage  of  1  diameter),  to  the  square 
inch ;  and,  to  calculate  the  strength  of  a  projecting 
beam,  this  quantity  should  be  multiplied  by  the  cross- 
section  and  the  depth,  and  the  product  divided  by  the 
distance  of  the  load  from  the  fulcrum,  [xciv.] 

For  the  safe  load  in  the  middle  of  a  beam  supported 
near  the  ends,  take  four  times  the  above  quantity 
(=  l,000fbs.),  multiply  by  cross-section  and  depth,  and 
divide  by  length  between  supports. 

A  beam  will  bear  twice  as  much  load  uniformly  dis 
tributed  over  its  length,  as  when  it  is  concentrated  in 
the  centre,  in  case  the  bea'.n  is  supported  at  the  ends, 
or  at  the  end  in  the  case  of  a  projecting  beam. 

But  these  are  familiar  principles  and  need  not  be 
dwelt  upon  in  this  place. 


278  BRIDGE  BUILDING. 

CLEAVAGE. 

CXLIII.  In  order  that  a  piece  of  timber  may  act  by 
tension,  it  is  necessary  that  a  portion  of  its  fibres  be 
separated,  to  form  a  heading  for  the  stretching  force  to 
act  against;  and,  that  the  strength  of  the  piece  may 
be  made  available  for  as  great  a  part  of  its  length  as 
may  be,  without  having  the  head  split  off,  it  becomes 
important  to  know  the  power  of  the  material  to  resist 
such  a  result. 

Let  ab  Fig.  54  represent  a  heading  by  means  of 
which  the  stick  is  made  to  act  by  tension.  Now,  as  the 
timber  is  incapable  of  supporting  upon  the  ends  of  its 
fibres  with  safety,  for  a  great  length  of  time,  a  force  of 
more  than  8  or  10  hundred  pounds  to  the  square  inch, 
the  area  ab  should  contain  at  least  one  square  inch-for 
each  l,OOOIbs.  to  be  applied  to  it.  And,  if  the  head 
ab  be  too  nigh  the  end  of  the  stick,  the  part  abed  will 


split  off,  and  be  thrust  over  the  end  of  the  timber.  It 
is  found  by  experiment  that  to  produce  this  effect  upon 
timber  of  sound  and  straight  grain,  requires  a  force  of 
nearly  GOOEbs.  to  the  square  inch  of  cleavage  in  the  area 
efcb.  It  is  therefore  obviously  necessary  to  safety,  that 
the  head  ab,  be  at  a  distance  from  the  end,  equal  to  at 
least  10  times  the  depth  (ae)  of  the  head,  that  the  area 
of  cleavage  may  be  sufficient  to  stand  as  great  a  force 
as  the  area  of  head  can  stand ;  i.  e.,  there  should  be 
10  inches  of  cleavage  surface  to  one  inch  of  head  surface. 


WOODEN  BRIDGES.  279 

If  the  heading  be  formed  in  the  central  part  of  the 
Btick,  as  by  a  mortice  or  pin  hole,  two  cleavages  must 
be  made  from  the  hole  to  the  end  in  order  that  the 
part  may  be  forced  out.  Hence,  the  hole  need  be  only 
about  five  times  the  width  of  hole  from  the  end  ;  that 
is,  an  inch  hole  should  be  five  inches,  and  a  two  inch 
hole,  10  inches  from  the  eud. 

TRANSVERSE  CRUSHING. 

Timber  is  sometimes  liable  to  be  crushed  by  forces 
acting  transversely  to  the  direction  of  its  fibres.  If 
the  pressure  be  applied  to  the  whole  sLle  of  the  piece, 
it  should  not  exceed  150,  or  at  most  2001bs.  to  the 
square  inch,  in  practice.  If  acting  on  one-half  of  the 
surface,  it  may  perhaps,  be  SOOSbs.  to  the  inch,  without 
yielding  very  injuriously  ;  and,  for  a  very  small  portion 
of  surface,  as  under  a  bolt  head  or  washer,  a  pressure 
of  500ft>9.  to  the  inch  may  be  admissible.  These  limits 
are  taken  with  reference  to  pine  timber.  Hard  timbers, 
will  bear,  probably,  25  to  50  per  C.  more  with  safety. 

CONNECTIONS  OF  TENSION  PIECES,  AND  PROPORTIONATE 
AMOUNT  OF  AVAILABLE  SECTION. 

CXLIY.  From  what  has  been  already  said,  it  fol 
lows  that  for  a  piece  to  act  with  the  best  advantage  by 
tension,  if  the  connection  be  made  all  at  one  point  in 
the  length,  one-half  of  the  fibres  require  to  be  cut  off, 
so  as  to  form  an  area  of  heading  equal  to  the  cross-sec 
tion  of  the  remaining  part  of  the  stick ;  since  it  has 
been  assumed  that  the  power  to  resist  tensile  strain 
with  safety,  is  the  same  as  the  power  to  resist  compres 
sion  upon  the  ends  of  fibres.  But  if  several  headings, 
or  shoulders  be  made  at  different  points,  or  distances 


280  BRIDGE  BUILDING. 

from  the  end,  a  less  portion  of  the  fibres  require  to  be 
separated. 

If,  upon  apiece  4  inches  thick,  instead  of  one  shoulder 
2  inches  deep  at  20  inches  from  the  end,  we  make  two 
of  one  inch  deep,  each,  the  one  at  10,  and  the  other  at 
20  inches  from  the  end,  we  have  the  same  area  of 
shoulder,  and  50  per  C,  more  fibres  to  act  by  tension  ; 
which  may  be  made  available  by  another  shoulder  at 
30  inches  from  the  end.  Thus  a  greater  proportion  of 
the  fibres,  but  a  less  proportion  of  the  length  is  availa 
ble. 

In  the  same  manner,  if  a  piece  be  connected  by 
pinning,  requiring  2  pins  of  2  inches  in  diameter,  at 
10  inches  from  the  end,  fourl  inch  pins,  two  at  5,  and 
two  at  JO  inches  (if  stiff  enough),  give  the  same  shoulder 
surface,  and  require  the  cutting  of  only  half  as  many 
fibres  ;  and,  two  more  pins  at  15  inches  from  the  end 
will  give  jths  of  the  whole  area  of  section  available  for 
tension.  In  case  the  smaller  pins  be  not  stiff  enough, 
they  may  be  of  an  oblong  section  in  the  direction  of 
the  strain. 

A  still  further  reduction  of  depth  of  shoulder  or 
width  of  pin,  will  make  a  still  larger  proportion  of  the 
fibres  available,  but  not  so  much  length  ;  and,  experi 
ence  and  judgment,  with  a  little  calculation,  must  dic 
tate  as  to  the  proper  medium  in  this  respect.  The 
theoretical  limit  is,  when  the  shoulders  are  infinitely 
small,  in  which  case,  the  whole  cross-section  becomes 
available.  But,  as  the  resistance  to  cleavage  must  be 
equal  to  the  force  of  tension,  it  follows  that  the  loss  in 
available  length,  is  proportional  to  the  amount  of 
cross-section  available  for  tension. 

In  practice,  it  is  usually  not  expedient  to  estimate 
more  than  one-half  or  two  thirds  of  the  whole  section 


WOODEN  BRIDGES  —  CONNECTING  PINS.        281 

as  available  for  tension.  This  reduces  the  safe  practi 
cal  strain  for  timbers  sustaining  tension,  to  from  500 
to  TOOlbs.  to  the  square  inch,  for  the  whole  cross-section ; 
and  the  proper  point  between  these  limits  should  be  de 
termined  by  the  mode  of  forming  the  connections  in 
specific  cases. 

PINS  OF  WOOD  AND  IRON,  FOR  CONNECTING  TIMBERS 
IN  BRIDGE  WORK. 

CXLV.  Perhaps  no  more  suitable  place  will  occur 
for  making  a  few  general  remarks  upon  the  merits  and 
use  of  pins  for  connecting  pieces  of  timber. 

While  it  is  readily  admitted  that  the  plank  lattice 
girder,  put  together  exclusively  with  wooden  pins,  an 
swered  an  excellent  purpose  in  affording  cheap  and 
serviceable  bridges  in  this  country  when  timber  was 
abundant,  and  the  iron  manufacture  in  its  infancy,  it 
is  nevertheless  believed  that  the  use  of  wooden  pins  in 
bridge  construction,  is  not  destined  to  a  long  continu 
ance.  Where  pins  are  required  in  wooden  bridge 
work,  it  is  thought  that  iron  may  be  used  with  a  de 
cided  advantage  over  wood  —  not  in  the  lattice  bridge 
of  the  usual  form,  composed  of  a  great  number  of  dia 
gonals,  and  a  legion  of  connecting  pins  ;  but  in  a  modi- 
lied  form  (as  in  Figures  13  and  19),  with  a  greatly 
reduced  number  of  pieces,  and  points  of  connection. 

Wooden  pins  for  the  purpose  under  consideration, 
do  not  possess  sufficient  strength  in  proportion  to  the 
surface,  unless  made  so  large  as  to  require  too  much 
cutting  of  the  timber.  Moreover,  the  action  upon  the 
pin  tends  to  crush  it  laterally,  in  which  direction  the 
hardest  timbers  available  for  pins,  scarcely  offer  as 
much  resistance  as  the  ends  of  fibres  to  which  they  are 
opposed. 

36 


282  BRIDGE  BUILDING. 

Where  pieces  are  connected  with  their  fibres  paral 
lel,  wooden  pins  or  keys  with  cross-sections  elongated 
in  the  direction  of  the  grain,  to  give  them  the  necessary 
strength,  may  be  employed  without  too  much  cutting 
of  the  timber.  Bat,  as  just  remarked,  the  key  is  liable 
to  yield  before  the  cut  ends  of  the  fibres  are  taxed  to 
their  full  capacity.  It  is  therefore  poorly  adapted  to 
the  purpose  in  any  case  where  great  strength  is  required. 
Moreover,  when  the  pieces  to  be  connected  are  placed 
across  one  another,  the  hole  will  not  admit  of  elonga 
tion  without  too  much  cutting  of  at  least  one  of  the 
pieces. 

If  it  be  required  to  connect  a  piece  by  a  pin  between 
two  other  pieces  as  seen  in  Fig,  55,  upper  diagram, 
the  pin,  as  already  seen,  should  be  strong  enough  to 
bear  as  much  strain  as  the  opposed  surface  can  sustain. 
Now,  we  have  seen  that  this  can  scarcely  be  done  by 
wooden  pins.  Still  if  sufficiently  stiff,  they  may  yield 
somewhat  to  compression,  without  material  loss  of 
strength. 

Taking  the  transverse  strength  of  pin  timber  at 
SOOfts.  to  the  inch,  with  leverage  equal  to  diameter, 
the  expression  4  x  3000rf  -*-  1  (a  representing  the  cross- 
section,  d,  the  diameter,  and  /,  the  length  of  pin,  be 
tween  centres  of  outside  bearings),  gives  the  amount 
which  the  pin  will  bear  in  the  middle. 

"Now,  the  two  outside  pieces,  having  each  half  the 
thickness  of  the  centre  one,*  I  must  equal  1J  times 
the  thickness  (0,  of  the  middle  piece  ;  while  the  effect 

*  The  outside  hearings  may  be  regarded  as  concentrated  at  the  centres 
of  thickness  of  the  pieces,  while  the  stress 
of  the  pin  in  the  centre,  is  the  same  as  if 


'.T*;.  .  ..  :  .frjs-.'.  tne    force  exerted   by    the  middle  timber, 

•<•:<§»:  wore    concentrated    half   and    half   at  the 


I  ->>>-  :  ^>  }  centres  of  the  two  halves  of  the  piece  ;  see 

L-  —  -  ;  -  ^*  diagram. 


WOODEN  BRIDGES  —  CONNECTING  PINS.        283 

of  the  force  exerted  by  said  middle  piece,  is  two-thirds 
of  what  the  same  force  would  produce,  if  concentrated 
in  the  middle  of  the  pin,  and  consequently,  the  pin 
will  hear  50  per  C.   more.     Hence,  we  have  4xljx 
30(W-r-  lJ/,=  1200a</-5-<,=  strength  of  the  pin. 

But  the  opposed  surface  will  hear  1,000&/ ;  and  put 
ting  this  expression  equal  to  the  former,  and  deducing 
the  value  of  d,  in  terms  of  t,  it  will  show  the  smallest 
diameter  of  a  wooden  pin,  strong  enough  to  hear  as 
much  as  the  opposed  surface.  This  equation  gives 
d  =  1.03^;t  whence,  it  appears  that  the  wooden  pin 
should  he  3  per  C.  greater  in  diameter  than  the  thick 
ness  of  the  middle  timber. 

In  the  same  manner,  the  strength  of  an  iron  pin  in 
the  same  circumstances,  is  respresented  by  4xlJ 
X5,000ad  -*-  1J*,  =  20,000ad  -r- t,  which  made  equal  to 
l,000fr/,  gives  d  =  0.252£,  hence,  the  most  economical 
diameter  for  an  iron  pin  in  fastening  one  piece  between 
two  others,  is  about  Jth  the  thickness  of  the  middle 
piece;  i.  e.,  taking  the  stiffness  of  a  round  pin  at 
5,000ft)s.  But  reducing  it  to  4,500Ibs.  as  proposed  in 
another  place  [xcvm],  it  gives  c?  =  0.266^;  whence, 
even  upon  this  basis,  it  will  be  safe  in  practice  to  make 
d  =  |^,  and  the  whole  length  of  pin  «=  2£,  so  that  it  may 
extend  into  the  outside  pieces  to  the  extent  of  half  the 
thickness  of  the  middle  piece. 

Since  the  outside  pieces  (Fig.  55),  require  half  the 
thickness  of  the  middle  piece,  and  the  pin  requires  a 
diameter  equal  to  \t  =  J  the  thickness  of  outside  pieces, 
it  follows  that  in  pinning  or  spiking  a  plank  or  timber 
to  the  outside  of  a  thicker  piece,  the  pin  or  spike  should 

f  Dividing  tlie  equation  l2Q3ad-±-t  =-1,000^,  by  lOOd  and  multiply 
ing  by  t,  give  12a  —  I0t\  But  12<z  — 12x.7854da,  =9.4248da,  =  10ta- 
whence,  cf  —  1.06K9,  and  d— v/TOGl?"  =  1.03*. 


284 


BRIDGE  BUILDING. 


have  half  the  thickness  of  the  piece  attached,  that  it 
may  not  bend  with  less  force  than  the  ends  of  the 
severed  fibres  can  bear ;  and  should  extend  into  the 
thicker  timber  at  least  6  times  its  diameter.  For,  as 

FIG.  55. 


1    1    I    \ 

I 

1                 '            j             0             1 

B331 

| 

\          ik—  4K         \ 

ffcEEtt           ...^ 

the  inner  portion  of  the  pin  or  spike,  must  act  upon 
the  wood  in  the  same  direction  as  the  part  through  the 
attached  piece,  it  requires  the  same  amount  of  surface 
to  act  upon,  while  the  intermediate  portion  requires  a 
surface  equal  to  that  acting  upon  the  two  end  portions. 
And,  even  in  this  condition,  the  pressure  is  not  uniform 
upon  all  parts  of  the  length  of  the  pin,  since  there  is  a 
neutral  point,  as  represented  by  the  upper  dotted  line 
(lower  diagram,  Fig.  55),  where  the  pressure  changes 
from  one  side  to  the  other,  and,  near  this  point,  must 
be  very  light  in  both  directions.  Hence,  for  the  most 
perfect  results,  in  such  cases,  the  pin  should  probably 
enter  the  thicker  timber  to  a  distance  of  7  or  8  times 
the  diameter  of  the  pin. 

When  the  end  bearings  of  the  pin  act  transversely 
to  the  grain,  they  require  at  least  50  per  C.  more  ex 
tent  of  bearing,  or  even  twice  as  much,  when  practica 
ble.  At  50  per  C.  I  =  If/',  and  the  effect  of  the  pressure 
exerted  by  the  middle  piece,  is  ^ths  that  of  the  same 
force  at  the  centre  of  the  pin.  The  equation  for  the 
proper  diameter  of  the  pin,  then,  is  4x|x5,OOOfltfH-l}£ 
=  1,000/d ;  whence,  d  =  0.283*,  and  length  of  pin  =2H 


WOODEN  BRIDGES  —  SPLICING.  285 


SPLICING. 

CXLYI.  The  term  splicing,  as  applied  to  timber 
work,  may  be  defined  to  be  the  uniting  of  two  pieces 
of  timber  by  their  end  portions,  so  as  to  form  (in  figure) 
a  continuous  timber  upon  a  straight  axis. 

The  splicing  of  timber  to  withstand  a  thrust  action, 
requires  only  the  meeting  of  the  squared  ends  of  pieces ; 
or,  a  half  lap,  formed  by  removing  the  half  of  each  for 
a  foot  or  two,  more  or  less,  from  the  end,  and  lapping 
the  remaining  halves,  so  as  to  have  the  extreme  end  of 
each,  meet  the  shoulder  of  the  other. 

But  the  splicing  of  pieces  to  withstand  tension,  ob 
viously  requires  a  more  complicated  process ;  and, 
from  what  has  already  been  said,  [CXLIV,]  it  is  clear 
that  only  a  part  of  the  absolute  section  can  be  made 
available  to  withstand  a  tensile  strain. 

FIG.  56. 


In  Fig.  56,  we  have  the  profile  of  a  lock  splice,  by 
which  one-third  of  the  section  is  available  for  tension  ; 
the  depth  of  the  locking  being  equal  to  one-third  of 
the  thickness  of  timber.  Now,  that  the  locking  may 
not  split  off,  we  have  seen  that  the  lap  should  extend 
10  times  the  depth  of  lock,  each  way,  making  a  lap  of 
6§  times  the  thickness  of  the  timbers. 

By  slanting  the  timber  to  a  thickness  at  the  end  equal 
to  that  in  the  neck  of  the  lock,  we  lose  none  of  the 
cleavage  required  to  split  off  the  hook,  while  we  gain 
in  amount  of  section  where  it  is  required  for  bolt  holes 
to  secure  the  splicing.  Otherwise,  the  bolt  holes  would 


286  BRIDGE  BUILDING. 

reduce  the  available  section   below   one-third   of  the 
whole. 

It  is  proper  to  observe  with  regard  to  this  splice, 
and  also  the  succeeding  one,  that  the  power  being  ap 
plied  upon  the  reversed  shoulder,  or  hook,  out  of  the 
line  of  the  unbroken  fibres  which  resist  the  power, 
the  tendency  is  to  throw  tfye  ends  outward,  and  pro 
duce  a  degree  of  lateral  action,  which  weakens  the 
timber  to  a  somewhat  greater  degree  than  in  proportion 
to  the  amount  of  fibres  severed. 

FIG.  57. 


With  a  double  lock  splice,  as  in  Fig.  57,  one-half  of 
the  section  is  available.  This  requires  a  lap  of  10  times 
the  thickness  of  the  timber. 

By  three  lockings  upon  the  same  principle,  f  of  the 
fibres  may  be  utilized  for  tension,  with  a  lap  of  12 
thicknesses  (or  12£.),  and,  by  a  lap  13J£,  we  make  two- 
thirds  of  the  fibres  available.  Finally,  by  a  lap  of  20£. 
and  an  infinite 'number  of  lockings  the  whole  cross- 
section  would  be  available. 

But  this,  of  course,  is  a  point  not  attainable  in  prac 
tice.  From  J  to  J  —  say  an  average  of  J,  is  as  much 
as  can  be  reckoned  on,  and  about  as  much  as  can  usually 
be  made  available  for  tension,  at  the  end  connections 
of  a  single  timber. 

Splicing  may  also  be  effected  by  a  plain  scarf,  with 
bolting,  pinning  and  spiking,  as  indicated  in  Fig.  58. 
With  bolts,  pins  and  spikes  properly  arranged  and  pro 
portioned,  a  strong  splice  may  be  formed  in  this 


WOODEN  BRIDGES  —  SPLICING.  287 

manner,  with  a  less  lap  than  what  is  required  in  the 
lock  splice.     In  this  case  the  fastenings  should  pass 

FIG.  58. 


through  at  right  angles  with  the  plane  of  the  joint,  that 
they  may  not  be  slackened  by  a  slight  yielding  of  the 
timber  to  pressure,  in  the  holes.  This,  however,  is  a 
device  which  will  probably,  seldom  be  resorted  to  in 
bridge  construction. 

Timbers  may  also  be  shackled  together  end  to  end 
by  iron  bolts  and  straps,  as  shewn  in  Fig.  59.  The  ag 
gregate  cross-section  of  straps  should  be  about  1  square 
inch  to  each  10  to  15  thousand  pounds  of  strain  which 
the  splice  is  intended  to  bear;  and  the  diameter  of 
bolts  fastening  the  straps,  about  one-fifth  of  the  thick 
ness  of  timber,  to  secure  the  greatest  effect  for  the 
amount  of  section  destroyed  in  cutting  the  bolt  hole. 

FIG.  59 


To  connect  two  timbers  10x12  inches,  so  as  make 
half  of  the  fibres  available  for  tension,  we  may  take  6 
straps  2  feet  long  from  hole  to  hole,  and  containing  a 
cross-section  of  about  1  square  inch,  each.  Also  6 
bolts  of  2"  in  diameter,  and  arrange  the  straps  and 
bolts  as  shown  in  the  figure,  the  straps  being  placed 
upon  the  12"  sides.  This  will  cost,  say  for  ITOlbs.  of 
iron  at  7cts.,  $11.90. 


288  BRIDGE  BUILDING. 

The  expense  of  a  double  lock  splice  (Fig.  57),  will 

be  about  7  cubic  ft.  of  waste  timber, $3.50 

40Ibs.  of  iron  bolts,  washers  and  plates,...         2.80 
Labor  in  fitting  the  timbers,  say, 1. 

Total,,.... $7.30. 

showing  the  shackle  connection  to  be  from  4  to  5  dol 
lars  the  more  expensive. 

CONSTRUCTION  OF  WOODEN  TRUSSES. 

CLVII.  With  a  thorough  comprehension  of  the 
power  of  timber  to  resist  the  various  kinds  of  strain  to 
which  it  may  be  liable  in  bridges,  and  other  timber 
structures,  and  of  the  general  principles  of  forming 
connections  in  timber  work,  as  attempted  to  be  ex 
plained  and  get  forth  in  the  last  few  preceding  pages ; 
and  a  knowledge  of  the  general  forms  of  arrangement 
for  the  several  members  in  bridge  trusses,  or  girders, 
and  of  the  manner  of  computing  the  stresses  to  which 
the  several  parts  are  liable  to  be  subjected,  as  treated 
of  in  the  first  100  pages  or  so,  of  this  work,  the  details 
of  practical  construction  of  wooden  truss  bridges  may 
be  intelligently  entered  upon. 

Nothing  more  elaborate  will  be  here  undertaken, 
than  a  reference  to  general  forms  of  trussing  suitable 
for  wooden  bridges  of  different  spans,  and  a  descrip 
tion  of  what  seem  to  be  the  most  feasible  methods  of 
forming  connections  at  peculiar  and  specific  points. 

The  method  pursued  will  be,  to  proceed  from  the 
shorter  spans,  and  more  simple  combinations,  to  struct 
ures  of  greater  length,  and  requiring  a  greater  number 
and  a  more  complex  arrangements  of  parts. 


WOODEN  BRIDGES.  289 


Two  PANEL  TRUSSES. 

CLVIIT.  The  form  presented  in'  Fig.  3,  with  rafter 
braces  ad  and  dc,  and  a  tie  or  chord  ac,  together  with 
an  iron  tension  member  db  (in  1  or  2  pieces),  is  proba 
bly  the  best  adapted  to  bridges  from  20  to  25  feet  in 
length.  The  braces  should  meet  with  a  vertical  joint 
at  d  (Fig.  3),  and  toe  into  the  chord  tie  with  two  head 
ings,  and  one  or  two  small  bolts,  as  in  Fig.  60. 

Fia.  60. 


Assuming  the  brace  to  be  capable  of  sustaining  a 
thrust  of  500Ibs.  to  the  inch  of  section,  and  the  heading 
l,000ft)s,  to  the  inch,  the  aggregate  depth  of  heading, 
a/,  and  de,  should  be  one-half  the  depth  c6,  of  the  brace  ; 
and,  the  point  /,  should  fall  below  the  point  d,  by 
j\  ad,  so  as  to  give  a  length  of  cleavage  /A,  =  lOaf  or 
10  dh.  The  shoulder  de,  then,  should  be, 

(1),...  de  =J  cb  —  TV  ad,~$cb  —  hab  +  TV  db. 

We  here  speak  of  a  d  b  as  a  straight  horizontal  line, 
not  shown.  This  is  regarding  of  as  equal  to  the  verti 
cal  depth  of  cut  at  af;  which  will  be  sufficiently  near 
the  truth  for  our  present  purpose,  provided  the  brace 
be  not  very  steep. 

But  (2),...de  =  db.  sin.  dbe,  ~db.  sin.  cab. 
37 


290  BRIDGE  BUILDING. 

and,  putting  this  value  of  de  equal  to  the  one  above, 
and  changing  vulgar  to  decimal  fractions,  we  have, 

(3),  ..db.  sin.  cab  =*  0.5  cb  —  0.106  +  O.lr/6. 

Then,  transposing,  and  uniting  co-efficients  of  db. 

(4.). ..(sin.  cab—  0.1) </6  ==0.5c-6  — 0.106,  whence, 

,-v          ,,       0.5  cb  —  0.1  ab 

Now,  from  equation  (2)  we  derive  0*6=  sin  ca(),  which 
value  of  0*6  being  substituted  in  equation  (5),  we  have 

//>N  de  0.5  cb — Q.lab       \  ,,.    <,    .         , 

u  (6)»  -  sh^Tb  ~  sin.c^-o.1.  »  whence,   multiplying  by 
sin.  c06.  we  derive, 

(7),...  de  -  0-5^~^/5Then,  substituting  for  06,  its 

1     ^^_          *         r__, 

sin.  cab 

equal.  sin  cajb  the  last  equation  becomes, 


s 


Making  the  angle  C06  =  26°33J',  which  is  regarded 
as  a  suitable  inclination  for  the  brace,  being  one,  ver 
tical,  and  two,  horizontal  reach,  sin.  C06  «=  0.447,  which 
substituted  in  (8),  gives  de  «•  .356^6,  and  af=*  .144c-6. 

This,  it  will  be  recollected,  is  deduced  upon  the 
supposition  that  the  brace  will  sustain  a  compression 
of  500ft>s.  to  the  inch,  and  no  more  ;  which  will  depend 
upon  the  length  as  compared  with  the  least  diameter. 
If  the  brace  be  capable  of  bearing  with  safety,  more  or 
less  than  500ft>s.  to  the  inch,  the  heading,  or  butting 
surface  should  be  more  or  less  than  half  the  area  of 
cross-section,  in  like  proportion.  For,  if  unnecessarily 
large,  it  requires  too  much  cutting  of  the  chord,  and 
if  too  small,  the  pressure  upon  abutting  surfaces  be 
comes  too  great. 

With  the  inclination  of  brace  above  assumed,  the 
compression  upon  the  brace  obviously  equals  the  weight 


WOODEN  BRIDGES.  291 

sustained  multiplied  by  v/5  ;  and,  for  a  rail  road  bridge, 
at  1J  tons  to  the  lineal  foot,  the  weight  upon  each 
brace,  will  be  6,250ft>s.  =  %w ;  or  say,  J  (w  -f  W*)  = 
7,500ibs.  This  by  N/O,  gives  16,770ft>s.  =  thrust  of 
brace,  while  15,000ft>s.  =  tension  of  chord.  Now,  at 
SOOIbs.  to  the  square  inch  of  gross  section,  the  chord 
requires  30  square  inches,  and  the  brace  33J  inches* 
being  a  little  less  than  6"  square.  But  the  length  of 
brace  being  about  lift,  or  22  diameters  of  a  6"  stick, 
we  find  by  the  table  [CXLI],  the  brace  is  only  capable 
of  bearing  416ifes.  to  the  inch.  Hence,  with  a  6"  least 
diameter,  a  section  of  40.3  inches,  or  nearly  6"  x  1", 
becomes  necessary.  Still  the  butting  surface  required 
is  only  16.77  square  inches  —  a  little  less  than  2|-"  depth 
(at  right  angles  with  the  brace),  by  7"  in  width. 

This  2J  inches  in  depth  may  be  divided  between  the 
two  shoulders  at  a  and  d,  in  any  manner  that  will  leave 
a  length  of  cleavage  from  a  to  the  end  of  the  chord 
equal  to  10  a/,  or  more  strictly  10  afx  cos.  cab,  which 
equals  the  vertical  depth  of  cut  at/.  But  the  line  df, 
should  preserve  a  descent,  equal  to  J^-th  of  its  length. 

The  depth  of  shoulder  being  thus  reduced  from  Jc6 
(=  3"  in  this  case),  to  2|",  de  is  diminished  in  the  same 
degree,  and  from  .356c6,  becomes  |x.356c'6  =  .2966c6  ; 
and,  substituting  6"  for  c6,  we  have  de  =  1.78  inches. 
In  the  meantime  af  becomes  |x.!44c6,  =  .72". 

The  vertical  depth  of  cut  for  de,  =  1.78",  is  1.78xcos. 
cab,  =1.78x.894,  =  1.59".  Add  to  this  the  vertical  cut 
at/,  equal  to  .642"  and  it  makes  2.233",  =  aggregate 
vertical  depth  of  cut  in  the  chord,  whence  the  distance 
eg  should  be  22.33  inches,  to  afford  the  necessary  re 
sistance  to  cleavage. 

Now,  we  require  in  the  chord  15  square  inches  of 
unsevered  fibre,  to  withstand  the  horizontal  thrust  of 


292 


BRIDGE  BUILDING. 


the  brace  while  we  require,  as  seen  above,  1.59X 
7  =  11.13  inches  to  be  cat  away  to  form  foothold  for 
brace,  making  aggregate  section  of  chord  =  15+11.13 
=  26.13  sqr.  inches,  equal  to  about  7"  X  3£",  by  strict 
computation. 

Timbers  so  small,  however,  although  capable  of  sus 
taining,  without  excessive  stress,  any  action  to  which 
a  bridge  is  legitimately  exposed,  is  not  to  be  recom 
mended  in  practice,  as  the  structures  might  be  de 
stroyed  by  casualties  which  would  but  slightly  affect 
the  large  timbers  required  in  heavier  and  longer  struct- 
tures. 

The  centre  of  bearing  of  the  truss  upon  the  abut 
ment,  should  be  directly  under  the  point  i,  at  the 
meeting  of  central  axes  of  the  brace,  and  the  unsevered 
portion  of  the  chord.  Otherwise,  an  injurious  lateral 
strain  would  result  to  the  chord  at  its  weakest  point. 

The  transverse  beam  at  the  centre  of  the  truss,  may 
be  placed  above  the  chord  or  below,  as  preferred,  and 
sustained  by  2  suspension  bolts  descend 
ing  divergently  from  a  saddle,  or  double 
washer  at  the  vertex  of  the  braces,  pass 
ing  through  the  beam,  and  secured  by 
nuts  and  washers  upon  the  under  side  of 
the  beam,  as  shown  in  Fig.  61.  The 
divergence  of  bolts  should  be  from  Jth 
to  Jth  their  length,  and  the  section  of 
bolts,  a  trifle  more  than  what  is  required 
simply  to  sustain  the  weight,  as  they  may 
act  unequally,  in  consequence  of  a  small 
lateral  tendency  of  the  braces. 

A  small  bolt  should  pass  vertically 
through  chord  and  beam,  to  preserve 
them  in  place.     Also,  a  small  bolster,  or  corbel  block 


FIG.  61. 


WOODEN  BRIDGES.  293 

(j.  Fig.  60  and  61),  under  the  chord  at  the  end,  affords 
some  protection  at  the  weak  point  in  the  chord. 

A  pair  of  horizontal  X  braces  in  each  panel,  between 
beam  and  abutments,  or  plate  timbers  upon  abutments, 
are  required  to  produce  lateral  steadiness  in  the  struc 
ture. 

The  idea  of  constructing  the  trusses  of  a  rail  road 
bridge,  even  of  20'  span,  of  6"  timbers,  to  persons  in 
the  habit  of  seeing  such  bridges  constructed  with  tim 
bers  10  or  12  inches  square,  will  undoubtedly  suggest 
visions  of  catastrophe,  courts  and  coroners ;  and,  in 
view  of  liability  to  casualty,  fretting  at  joints,  and  per 
haps  surface  decay,  it  may  be  advisable  to  use  in  such 
structures,  timbers  somewhat  larger  than  the  above 
computations  indicate  as  sufficient  to  withstand  deter 
minate  forces. 

But,  as  an  instance  of  what  strength  may  be  obtained 
with  very  small  timbers,  properly  proportioned  and 
put  together,  it  may  be  here  stated  that  a  model  of  a 
20  feet  truss,  upon  a  scale  of  1  to  12,  constructed  as 
above  explained,  of  J"  x  T62"  braces  and  chord,  bore 
without  material  injury,  350ft>s.  at  the  centre,  equiva 
lent  to  700ft)S.  distributed,  and  representing  700x144 
=  100,800ft>s.  upon  one  truss,  or  over  100  net  tons  upon 
a  20  f^eet  bridge;  being  some  four  times  as  much  as  a 
single  track  rail  road  bridge  of  that  span  is  usually 
subjected  to. 

With  regard  to  the  proper  size  of  transverse  beam, 
the  formula  (see  rule  [CXLII]),  1^5±£  ==  W,  (a represent 
ing  area  of  section,  d,  depth  of  beam,  £,  length  between 
supports,  and  W,  the  load  in  the  centre),  gives  a  = 
iOMd"  Then,  assuming  I  =  15',  W  =  7,500ft>s,  (  = 
15,0001bs.  distributed),  and  d  =  14" ;  we  have  a  »= 


294  BRIDGE  BUILDING. 

lowxi"  =  96'4  square  inches  ;  which  divided  bv  dePth 
(d),  in  inches,  gives  thickness  (f),  =  7  inches  nearly. 

Or  the  formula  t  =  gives  the  required  thickness 

directly.  But  in  this  case,  I  and  dmust  express  length 
and  depth  in  inches,  since  the  co-efficient  of  d  (1,000) 
refers  to  square  inches  of  section.  Otherwise,  the  co 
efficient  must  be  multiplied  by  144  to  'make  it  refer  to 
the  square  foot  of  section  ;  in  which  latter  case  the 
value  of  t  will  be  obtained  in  feet.  • 

In  the  case  of  beams  to  sustain  rail  road  track,  we 
may  let  V  =  length  of  beam  exclusive  of  the  portion 
between  rails,  and  W  =  weight  upon  the  2  rails.  If 
I'  =  120"  and  W  =  25,000ft>s.,  and  d  =*  14"  the  above 


formula  becomes,  *  =  _  _  15.3  in. 


THREE  PANEL  TRUSS. 

CLIX.  A  three  panel  truss  bridge  of  wood  may  be 
constructed  upon  the  plan  shown  in  outline  by  Fig.  7. 
The  main  braces  a6and  a'b'  may  connect  with  the  chord 
in  the  same  manner  as  in  the  two  panel  truss  described 
in  the  last  section,  and  illustrated  by  Fig.  60;  while 
the  upper  end  may  be  square,  and  the  whole  bevel  to 
form  the  angle  abb',  given  to  the  member  bb'.  Or,  the 
bevel  may  be  upon  both  members  ;  in  which  case  the 
saddle  plates  at  b  and  be  should  extend  over  the  joint, 
so  as  to  throw  a  part  of  the  weight  directly  upon  the 
brace.  In  case  the  bevel  be  all  upon  bb',  the  saddle 
need  not  bear  upon  the  brace. 

The  counter  braces  in  the  middle  panel  may  box 
into  the  chord  and  the  horizontal  W,  in  the  manner 
shown  in  Fig.  62,  either  by  the  black  or  the  dotted 
lines  ;  the  upper  end  of  the  counter  toeing  against  the 


WOODEN  BRIDGES.  295 

end  of  the  main  brace,  when  the  form  of  connection 
shown  by  the  black  line  is  used. 

As  the  counter  braces  cross,  or  meet  in  the  centre  of 
the  panel,  one  may  be  in  two  pieces  thrusting  into  the 
other  as  at  c  Fig.  62  ;  or  one  member  may  be  in  two 
full  length  pieces,  and  the  other  a  single  brace  between 
the  former,  of  such  width  vertically,  as  to  possess  the 
required  cross-section  ;  say  2J"  x  6"  for  the  outside, 
and  4x8  for  the  middle  one,  and  the  whole  connected 
by  a  small  transverse  bolt  at  the  crossing. 


The  stresses  of  the  several  parts  of  the  truss  may  be 
determined  in  the  manner  explained  in  section  xvni, 
and  the  timbers  proportioned  accordingly,  and  in  con 
formity  to  rules  in  relation  to  strength  of  timber  [CXL 
and  CXLI].  For  a  truss  of  30  feet  to  carry  a  gross  load 
of  15,000ft)3.  to  the  panel,  with  a  horizontal  reach  of 
brace  equal  to  twice  the  vertical  —  chord  and  "  strain 
ing  beam,"  (66',  Fig.  7),  should  be  7"  deep  x  9"  wide ; 
main  braces  8"  X  9".  Counter-braces  being  subject  to 
only  one-third  of  the  movable  panel  load,  may  properly 
be  4  X  8  or  5  X  6,  if  one  be  severed  at  the  crossing,  or 
as  above  specified,  if  one  member  be  in  2  full  length 
pieces. 

Two  counter-braces  might  cross  one  another  side  by 
side,  but  this  would  not  produce  a  well  balanced  action. 


296  BRIDGE  BUILDING. 

Bridges  of  this  length  of  span  are,  moreover,  often 
built  with  counter  braces  omitted,  for  common  road 
purposes.  But  such  practice  is  defective,  unless  extra 
depth  of  section  be  given  to  the  lower  chord,  so  that 
its  stiffness  may  transfer  a  portion  of  weight  over  the 
quadrangular  middle  panel ;  and  in  no  case  is  it  ad 
visable  to  dispense  with  counter  braces  in  a  rail  road 
bridge  of  three  panels. 

Beams  may  be  suspended  by  divergent  bolts  as  in 
Fig.  61,  and  bolted  to  the  chord;  while  horizontal  x 
ties  or  braces,  as  may  be  preferred,  in  each  panel  will 
prevent  lateral  swaying  of  the  structure. 

The  above  is  probably  the  simplest  and  best  plan  of 
wooden  truss  for  bridges  of  30  to  35  feet  span. 

FOUR  AND  Six  PANEL  TRUSSES. 

CLX.  The  same  general  arrangement,  with  the  same 
kind  of  connections,  in  trusses  of  4  or  6  panels,  accord 
ing  to  length  of  span,  may  be  used  with  good  effect 
for  common  road  purposes,  in  any  length  up  to  70  or 
80  feet.  In  such  cases,  each  panel  should  have  one 
main  brace,  and  counter  braces  may  be  entirely  omitted; 
as  the  partial  movable  load  is  seldom  so  great  as  to 
neutralize  the  action  of  weight  of  structure  upon  the 
main  braces. 

In  the  6  panel  truss,  the  movable  must  exceed  the 
permanent  panel  load  upon  the  two  beams  next  either 
end,  with  no  movable  load  upon  the  other  beams,  in 
order  to  neutralize  the  constant  tendency  to  action 
upon  the  central  pair  of  main  braces.  This  is  obvious 
from  the  fact  that  the  greatest  tendency  to  tension  action 
upon  the  latter,  is  3i0",  =  Jt0,  while  the  permonent  load 
gives  a  constant  opposite  tendency,  equal  to  JM?'. 
Should  such  cases  occur,  the  transverse  stiffness  of 


WOODEN  BRIDGES. 


297 


both  upper  and  low  chords  must  he 
overcome  before  a  collapse  could 
take  place.  In  the  case  of  iron 
trusses,  the  chords  are  supposed  to 
have  no  lateral  stiffness  at  the 
nodes;  consequently, counterbraces, 
or  ties,  as  the  case  may  be,  are  al 
ways  necessary  in  one  or  two  panels 
each  side  of  the  centre. 

Fig.  63  represents  a  Six  Panel 
truss,  as  arranged  and  recommended 
by  the  author  16  or  18  years  ago, 
and  adopted  by  the  Canal  depart 
ment  of  the  State  of  ]$few  York, 
for  farm  and  country  road  crossings 
over  the  State  canals,  upon  which 
several  hundreds  of  them  are  in  use. 

The  arrangement  of  upper  and 
lower  chord  timbers,  and  the  diver 
gent  suspension  rods,  to  maintain 
the  erect  position  of  trusses,  as  well 
as  the  assignment  of  correct  pro 
portions  to  all  the  parts  throughout, 
are  believed  to  have  originated  with 

O 

the  author  of  this  work. 

The  lower  and  longer  portion  of 
the  bottom  chord,  is  usually  in  two 
pieces,  spliced  with  double  locking 
and  bolting  (see  Fig.  57),  over  the 
centre  beam.  Transfer  blocks  are 
also  inserted  between  upper  and 
lower  timbers,  to  transfer  a  part  of 
the  stress  of  the  longer  to  the 
shorter  portion,  and  thus  dimmish 
the  strain  at  the  splicing. 


298  BRIDGE  BUILDING. 

The  long  portion  of  the  upper  chord  may  also  be 
in  two  pieces  meeting  with  squared  ends,  or  with  a 
plain  half  lap,  of  a  foot  or  so.  Transfer  blocks  or 
packing  pieces  and  bolts  should  likewise  be  inserted  as 
indicated  in  the  figure. 

The  dimensions  of  the  several  members,  of  course, 
will  depend  upon  the  length  and  depth  of  truss,  and 
the  load  it  is  required  to  bear.  It  is  seen  by  pro 
cesses  explained  heretofore  [XL  and  LIII],  that  the 
portion  of  chord  under  the  triangular  end  panels,  and 
also  the  endniost  sections  of  the  upper  chord,  are  liable 
to  action  equal  to  2JW-,  in  which  expression  "W  = 
w+w',  h  =the  horizontal,  and  v  =  the  vertical  reach 
of  braces.  The  next  sections  (top  and  bottom),  are 
liable  to  4W-,  and  the  lower  chord  under  the  two 

V 

middle  panels,  to  4JW-. 

The  end  braces  are  liable  to  2JW  \/A2  -f  v'2-i-v,thQ 
next  braces,  to  (lOu/'+lJw')  v/A2  -f  v2  -s-  v,  and  the 


middle  ones,  to  (6w"+%wf)  V  h?  -f  v2  -*•  V,  while  the 
verticals  are  exposed  to  2JW  for  the  endniost,  1W  for 
the  middle,  and  10  w"  -f-  IJw'  for  the  intermediates. 

Now,  we  have  only  to  assign  specific  values  to  w  and 
w',  and  to  A  and  v,  in  order  to  obtain  the  actual  maxi 
mum  stresses  the  several  parts  are  liable  to,  from  the 
general  expressions  just  found. 

Let  A  =  12',  and  v  =  7'  ;  which,  though  not  an  eco 
nomical  proportion,  as  we  have  seen  [LXIV],  may  be 
admissible  for  bridges  of  light  burthens,  giving  a  better 
appearance,  and  the  structure  being  less  top  heavy. 

The  weight  of  a  light  superstructure  of  this  descrip 
tion,  is  18  or  20  tons  —  say,  w'  =  3,000fbs.  Then,  as 
suming  w  =  6,000ft)s.  which  will  be  sufficient  for  the 


WOODEN  BRIDGES.  299 

lighter  class  of  private  and  country  bridges.     Then,  -  = 

V  =  1,714,  and  x//7~+~^H-  v  =  1.984. 

Substituting  these  values  in  the  above  expressions 
for  stresses,  we  have  2J  X  9,000  X  1.714,  =  38,565,  = 
tension  of  end  section  of  bottom  chord.  For  the  next 
section,  4  X  9,000  X  1,714  =  61,704ft>s. ;  and,  for  the 
two  middle  sections,  69,417ft>s. ;  while  the  compression 
of  the  two  portions  of  the  upper  chord,  is  38.565flbs., 
for  the  end,  and  61,7041bs.,  for  the  middle  sections. 

The  maximum  compression  of  the  three  sets  of 
braces,  is  44,653  for  the  ends,  14,880  for  the  middle 
ones,  and  28,760  for  the  intermediates. 

The  tension  of  suspension  bolts,  is,  at  the  maximum, 
for  the  endmost  22,500,  for  the  middle  ones,  9,000 
(  =  W),  and  for  the  intermediates  14,500. 

The  main  portion  of  the  lower  chord,  requires  a  lap 
at  the  splice,  equal  to  10  times  its  depth,  [CXLVI.] 
Hence,  the  less  depth,  the  less  waste  in  splicing,  and 
the  more  lateral  stiffness  of  truss.  But  this  also  in 
volves  greater  required  section  in  the  lighter  braces, 
which  become  too  thin,  vertically,  to  act  with  advantage 
under  compression. 

There  is  no  ready  means  of  determining  the  exact 
optimum  in  the  ratio  of  depth  to  width  of  timbers  in 
this  case  ;  and  we  shall  not  err  greatly  by  assuming  a 
ratio  of  width  to  depth  as  3  to  2,  or  as  4  to  3  ;  neither 
to  be  rigidly  adhered  to. 

The  bottom  chord  may  suffer  tension  in  the  second 
panel,  equal  to  nearly  62,000ft>s.,  requiring  62  inches 
of  net  section  ;  while  the  second  brace  has  a  maximum 
horizontal  thrust  of  nearly  25,000ft>s.,  requiring  the 
severing  of  25  inches,  whence  this  part  of  the  chord 
should  have  a  gross  section  of  62  +  25,  =  87  inches. 


300  BRIDGE  BUILDING. 

This  amount  may  be  furnished  nearly,  by  a  section  of 
8£"  x  10",  8  x  11,  or  7  x  12.  Assuming  the  second, 
the  end  braces  should  be  8-J  X  11,  the  next  7  x  11,  and 
the  middle  ones,  5J  x  11. 

We  have  seen  above,  that  62,000ft>s.  of  tension,  are 
communicated  to  the  long  timbers  of  the  lower  chord, 
while  the  splice  at  the  middle  is  only  good  for  500ft>s., 
to  the  inch  of  gross  section,  being  44,000ft)3. ;  thus 
leaving  a  deficiency  of  18,000ft)3.  to  be  sustained  and 
made  up  by  the  upper  timber.  In  the  mean  time, 
the  middle  braces  exert  about  8,OOOIbs.  of  horizontal 
action  upon  this  piece,  under  a  full  load  of  the  truss, 
and  near  13,000ft>s.  at  the  maximum  action  of  those 
braces.  Hence  that  timber  should  have  a  mini n urn 
net  section  of  26  inches,  -f  18  inches  to  be  severed  for 
the  insertion  of  transfer  blocks.  The  timber  should 
therefore  be  at  least  4"  deep. 

The  transfer  blocks  should  be  If "  thick,  in  this  case, 
and  15  or  16  inches  long,  and  be  well  fitted  in  position 
as  indicated  in  Fig.  63.  This  mode  is  preferable  to  that 
of  using  blocks  twice  as  thick,  and  letting  one-half  into 
each  timber  by  a  square  boxing;  because  it  leaves  a 
larger  section  of  timber  opposite  the  middle  of  the 
block  where  bolt-holes  are  required.  Otherwise  it 
would  be  necessary  to  provide  additional  gross  section 
on  account  of  bolt  holes.  The  same  reason  applies  in 
the  case  of  braces  toeing  into  chords,  &c. ;  where  the 
boxing,  instead  of  being  as  deep  at  the  heel  as  at  the 
toe  of  the  brace,  should  taper  out  to  nothing  at  the  heel. 
See  black  line  at  foot  of  counter  brace  c,  Fig.  62. 

This  case  has  been  given  in  pretty  full  detail,  since 
the  plan  seems  to  merit,  as  it  certainly  enjoys,  a  high 
degree  of  popularity,  for  small  bridges  for  ordinary  use. 


WOODEN  BRIDGES.  301 

By  increasing  the  depth  to  at  least  Jth  of  the  length 
of  truss,  inserting  counter  braces  in  the  two  middle 
panels,  and  proportioning  members  to  the  respective 
strains  to  which  they  are  liable ;  this  plan  is  undoubt 
edly  well  adapted  to  rail  road  purposes  in  spans  from 
50  to  70  feet  in  length. 

For  greater  spans  than  70  feet  for  rail  roads  and  80' 
for  common  roads,  higher  trusses,  with  top  connections 
and  lateral  bracing  or  tying,  should  undoubtedly  be 
adopted. 

CLXI.  The  bridge  usually  designated  asBeardsley's 
Bridge,  is  identical  with  the  one  shown  in  Fig.  63, 
modified  by  the  substitution  of  iron  bottom  chords, 
composed  of  two  parallel  rods  (to  each  truss)  in  5  pieces 
or  parts  corresponding  in  size  with  the  stresses  of 
chords  under  respective  panels.  The  middle  and 
largest  part  extending  under  the  two  middle  panels, 
and  the  others,  each  under  one  panel  only. 

These  pieces  or  parts,  being  connected  by  turn-buck 
les,  or  screw  couplings,  pass  through  cast  iron  shoes, 
into  and  against  which  the  several  braces  toe  and 
thrust ;  the  shoes  being  prevented  from  sliding  out 
ward  upon  the  rods,  by  the  couplings. 

The  shoe  should  in  all  cases  be  so  formed  and  located 
that  the  axes  of  action  of  chord,  brace  and  vertical, 
meet  at  the  same  point,  as  it  regards  the  intermediates, 
while  as  to  those  upon  the  abutments,  the  axes  of  chord 
and  brace  should  meet  over  the  centre  of  bearing  upon 
abutments. 

This  arrangement  (understood  to  have  been  the  sug 
gestion  and  device  of  Mr.  Geo.  Heath),  gives  very  sat 
isfactory  results,  and  the  only  practical  question  with 
regard  to  it,  as  compared  with  the  one  with  wooden 


302  BRIDGE  BUILDING. 

chords,  seems  to  be  merely  one  of  economy  and  con 
venience.  If  suitable  timbers  for  chords  can  be  readily 
and  reasonably  obtained,  it  is  thought  to  be  quite  as 
advantageous  to  use  wooden  chords. 

THE  HOWE  BRIDGE. 

CLXII.  A  very  popular  plan  of  wooden  bridges, 
which  has,  in  fact,  superseded  most  others  in  New  York 
and  New  England  for  rail-road  purposes  from  the  time 
of  the  introduction  of  the  rail  road  system,  is  known 
as  the  Howe  Bridge. 

The  trusses  have  upper  and  lower  parallel  chords, 
together  writh  main  and  counter  braces,  of  wood,  tied 
vertically  by  wrought  iron  tension  rods  from  chord  to 
chord,  the  principle  of  action  being  the  same  as  in  the 
plan  shown  in  Fig.  63. 

The  braces  act  upon  the  chords  and  verticals  through 
the  medium  of  cast  iron  shoes  or  skewbacks,  with  ribs 
or  flanges  let  into  the  chords  to  a  sufficient  depth  to 
sustain  the  horizontal  thrust  of  braces,  and  with  tubes, 
or  hollow  processes,  square  externally,  and  having 
round  holes  to  receive  the  vertical  bolts.  These  tubes 
project  downward  through  the  lower,  and  upward 
through  upper  chord,  between  the  courses  of  timber 
composing  the  chord,  being  boxed  into  the  timber  on 
each  side  of  the  tube,  so  as  to  leave  about  an  inch  be 
tween  adjacent  courses  for  ventilation ;  the  tubes,  ex 
tending  through  the  chords,  reach  an  iron  plate  upon 
the  opposite  side,  which  serves  as  a  washer,  or  bearing 
for  the  nuts  of  the  suspension  bolts. 

By  this  means  the  vertical  action  of  braces  is  brought 
directly  upon  the  verticals,  without  a  transverse  crush 
ing  action  upon  the  chord  timbers. 


WOODEN  BRIDGES. 


303 


The  chords  are  formed  of  3  or  4  courses  of  timber 
side  by  side,  with  a  depth  equal  to  two  or  three  times 
the  thickness;  the  joints  in  the  several  courses  being 
so  distributed  that  no  two  courses  may  have  a  joint  in 
the  same  panel  when  avoidable. 

Fig.  64,  represents  a  side  view  in  the  upper,  and  a 
top  view  in  the  lower  diagram,  of  a  portion  of  the  bot- 

FIG.  64. 


torn  chord.  At  t  is  represented  a  view  of  the  tube  of 
the  skewbackas  it  would  appear  with  the  outside  chord 
timber  removed  ;  at  m  m,  the  seats  of  the  main  braces, 
and  c,  the  seat  of  the  counter  brace.  Over  a,  is  a 
clamp,  or  lock  piece,  and  bbr  are  transfer  blocks,  or 
packing  pieces,  to  secure  the  joint,  and  transfer  the 
strain  from  one  to  another  of  the  chord  timbers.  The 
transfer  blocks  may  be  placed  obliquely  as  at  6,  or 
straight,  as  at  &'.  The  latter  is  the  more  usual,  but 
the  former  leaves  the  greater  section  of  timber  at  the 
point  where  the  bolt  holes  occur. 

The  braces  are  usually  placed  with  a  horizontal  about 
half  as  great  as  the  vertical  reach,  and  extending  across 
one  panel  only.  Counter  braces  used  throughout,  and 
the  upper  chord  made  of  equal  leugth  with  the  lower, 
giving  the  truss  a  rectangular,  instead  of  a  Trape 
zoidal  form. 


304  BRIDGE  BUILDING. 

Now,  it  is  obvious  that  in  a  rectangular  truss,  as 
represented  in  Fig.  52,  the  end  posts,  and  one  panel- 
length  of  the  upper  chord  at  each  end,  as  well  as  one 
counter-brace,  are  entirely  useless,  as  it  regards  sus 
taining  weight  of  structure  and  load.  It  will  readily 
be  seen,  moreover,  that  no  counter-braces  except  those 
of  the  two  middle  panels,  in  the  8  panel  truss,  Fig.  52, 
have  any  sustaining  action,  unless  the  variable  exceed 
4  times  the  permanent  load  of  the  truss. 

It  is  furthermore  manifest  that  there  is  a  large 
amount  of  surplus  material  in  the  portions  of  lower 
chord  toward  the  ends  ;  the  tension  of  that  chord  being 
in  the  several  panels,  preceding  from  the  end  (in  the 
case  of  Fig.  52),  as  3J,  6,  7J  and  8.  Hence,  over  one- 
fifth  of  the  material  in  a  chord  of  uniform  section,  is  in 
excess. 

But  the  greatest  sacrifice  of  economy  in  the  Howe 
Bridge  as  usually  constructed,  results  from  the  steep  pitch 
of  the  braces.  For,  while,  as  was  seen  [LXVI],  braces 
act  with  about  the  same  economy  at  an  inclination 
giving  a  horizontal  reach  equal  to  the  vertical,  as  when 
the  former  equals  only  one-half  of  the  latter,  that  is, 
with  h  =  v  and  h  =*  Jy,  it  was  shown  in  the  succeeding 
section,  that  the  action  upon  verticals  was  nearly  twice 
as  great  in  the  latter,  as  in  the  former  case.  For  in 
stance,  suppose  Fig.  18  to  represent  a  16  panel  trnss, 
with  thrust  braces  and  tension  verticals.  Estimating 

O 

successively  the  action  upon  verticals  with  diagonals 
crossing  two  panels,  as  in  Fig.  18,  and  the  same  with 
diagonals  crossing  but  one  panel,  we  find  the  action 
over  85  per  cent  more  in  the  latter  than  in  thet former 
case. 

"With  regard  to  chords,  the  horizontal  effect  is  essen 
tially  the  same  in  both  cases,  while  the  vertical  thrust 


WOODEN  BRIDGES.  305 

of  braces,  being  but  little  over  half  as  great  witb  the 
long,  as  with  the  short  horizontal  reach,  may  be  sus 
tained  by  the  timber  of  the  chord,  thus  obviating  the 
necessity  of  tubes  extending  through  the  chord  from 
the  cast  iron  skewback;  and  furthermore,  may  enable 
the  iron  shoe  to  be  dispensed  with  altogether,  in  many 
cases.  Hence  would  result  a  still  further  saving  in  ex- 

o 

pense,  as  well  as  in  weight  of  structure. 

Take,  for  example  a  brace  10"  square,  capable  of 
resisting  a  tnrust  of  50,0001bs.  in  the  direction  of  its 
length,  and  a  vertical  pressure  of  35,0001bs.  when  in 
clined  at  45°.  "Whether  the  end  be  cut  as  at  d,  e,  or/ 
(Fig.  64),  it  covers  a  horizontal  area  of  141  square 
inches,  giving  a  square  inch  for  every  250Ibs.  of  vertical 
pressure.  This  does  not  much,  if  any,  exeeed  the  ca 
pacity  of  timber  for  resisting  transverse  crushing,  as 
estimated  in  section  CXLIII,  when  acting  upon  a  portion 
of  surface  so  limited  with  respect  to  the  whole. 

Perhaps,  however,  the  propriety  of  dispensing  with 
the  iron  shoe,  should  not  be  too  strenuously  urged. 
But  there  seems  to  be  little  excuse  for  incurring  the 
sacrifice  of  iron  required  in  suspension  bolts  in  case  of 
the  steep  braces,  over  what  is  required  with  the  greater 
inclination.  The  interference  of  bolts  with  braces, 
when  the  latter  reach  across  two  panels,  is  perhaps  the 
greatest  obstacle  in  the  way  of  adopting  the  latter  ar 
rangement  ;  and  this  may  be  managed  by  either  pass 
ing  the  bolts  through  the  intervening  braces  (which 
does  not  materially  impair  their  strength,  when  sup 
ported  at  intervals  by  counter-braces),  or  between 
main  and  counter  braces,  as  may  seem  most  favorable  • 
in  respective  cases, 

In  view  of  the  above  considerations,  the  author  can 
not  avoid  regarding  the  usual  practice  in  the  construc 
tion  of  Howe  Bridges,  as  decidedly  faulty. 


306  BRIDGE  BUILDING. 


TRAPEZOID  WITHOUT  VERTICALS.* 

CLXIII.  This  form  of  truss,  Figs.  13,  15  and  19,  has 
been  shown  [XLIV,  &c.],  to  be  liable  to  a  less  amount 
of  action  upon  materials,  in  sustaining  a  given  load 
under  like  general  conditions,  than  any  of  the  other 
forms  analyzed  in  this  work;  and  this  advantage  may 
be  made  practically  available  in  wooden  bridge  con 
struction,  by  a  system  of  chords  and  diagonals  con 
nected  by  transverse  iron  bolts  and  pins  at  the  nodes 
of  upper  and  lower  chords. 

The  lower  chords  should  be  proportioned  in  their 
several  parts,  nearly  in  accordance  with  the  stresses  to 
which  such  parts  are  liable.  This  may  be  accomplished 
by  a  pair  of  parallel  courses  of  timber  of  uniform  sec 
tion  upon  the  outsides  of  the  chord  from  end  to  end, 
placed  at  such  distance  asunder  as  to  admit  the  ends 
of  diagonals  between  them,  and  also,  to  admit  of  addi 
tional  courses  of  chord  timbers  upon  the  inside  of  the 
former,  to  be  introduced  as  required  toward  the  centre, 
to  give  in  each  panel  a  section  of  chord,  proportional 
to  the  computed  strain  for  such  part. 

The  pieces  composing  the  several  courses,  may 
be  spliced  with  the  double  lock,  Fig.  57,  usually  with 
the  centre  of  the  splice  at  the  nodes,  or  connecting 
points  of  chords  with  diagonals ;  no  two  splices  in  the 
same  half-chord  to  occur  at  the  same  node. 

The  upper  chord  should  be  increased  in  section  by 
enlargement  of  the  section  rather  than  the  number  of 
courses.  Or,  in  some  cases,  timbers  may  taper  in 
thickness  toward  the  ends  of  chords,  either  upper  or 

*  The  characteristic  of  this  truss,  is  not  that  strictly  speaking1  it  lias 
no  vertical  members,  but  that  there  is  no  general  alternate  transfer  of 
•weight  from  diagonals  to  verticals,  and  the  contrary. 


WOODEN  BRIDGES.  307 

lower.  For  instance,  if  5"  in  thickness  be  sufficient 
in  the  end  panel,  and  7"  be  required  in  the  next,  a 
timber  extending  over  the  width  of  two  panels,  6"  at 
the  smaller,  and  8"  at  the  larger  end,  will  answer  the 
requirement  with  perhaps  less  waste  of  timber  and 
labor  than  would  suffice  under  a  different  arrangement. 
But  such  matters  must  be  left  to  the  judgment  of  the 
designer. 

The  upper  chord  acting  by  compression,  the  timbers 
may  be  connected  by  a  half-lap  of  1J  or  2  feet  at  the 
nodes,  where  the  main  connecting  bolts  will  secure 
the  ends. 

The  diagonals  which  act  principally  by  compression 
(represented  as  the  narrower  ones  in  Figs.  65  and  66), 
may  be  in  pairs,  while  those  mostly  exposed  to  tension 
(the  wider  ones),  may  be  single,  and  placed  between 
the  former.  Thus  usually  three  pieces  are  united  at 
each  node. 

FIG.  65. 


.. 

V  ?/  \ 

/  w 


In  some  cases  where  the  thickness  of  diagonals  ex 
ceeds  the  space  between  half-chords,  the  thrust  dia 
gonals  may  be  shouldered  to  fit  a  boxing  upon  the  in 
side  of  the  chord ;  as  by  either  of  the  vertical  dotted 
lines,  Fig.  65.  Sometimes  also,  the  boxing  may  ex 
tend  through  the  whole  depth  of  the  chord,  so  as  to 
require  no  cutting  of  the  diagonal ;  and  again,  the 
thickness  of  the  diagonals  maybe  reduced  in  the  parts 


308  BRIDGE  BUILDING. 

between  chords,  and  no  cutting  of  chord  timbers  re 
quired.. 

"When  cutting  of  timbers  becomes  necessary  for  pur 
poses  as  above,  it  should  be  in  the  parts  where  the 
greater  surplus  over  the  necessary  net  section  occurs, 
whether  in  chord  or  diagonals.  Every  part  should 
have  a  square  inch  of  net  available  section  for  each 
l,0001bs.  of  tension,  and  a  square  inch  of  bearing  upon 
bolt,  pin,  or  shoulder,  for  each  l,OOOSbs.  of  either  ten 
sion  or  thrust  to  which  the  part  is  liable ;  and  the 
bearing  upon  bolts  and  pins  should  be  estimated  as 
equal  to  the  diameter  multiplied  by  the  length  of  hole 
through  the  piece ;  or,  equal  to  the  section  of  timber 
severed  by  the  hole. 

CLXIY.  Fig.  66  is  a  general  representation  of  the 
half  of  an  8  panel  truss,  suitable  for  a  100  foot  common 
road  bridge.  Let  v  —  14',  =  distance  between  centres 
of  upper  and  lower  chords,  and  h  =  12 J',  =  horizontal 
width  of  panel.  Then,  assuming  w  —  10,0001bs. 
(=  movable  panel  load),  and  wf  =  4,000ft>s.  (=  perma 
nent  panel  load),  we  have  -  =  .893  (nearly),  and  D  = 

18.77'  =  length  of  diagonal;  whence,  D-  =  1.34;  and, 
computing  the  stresses  of  the  several  parts  and  mem 
bers  by  the  process  explained  in  sections  [XLIV,  &c.,], 
the  maximum  vertical  pressure  at  a  equals  49,000ft>s. 
giving  a  longitudinal  compression  upon  ai9  equal  to 
65,660Bbs.,  and  a  tension  upon  ab,  equal  to  43,750ft>s. 

For  the  double  member  ai,  8"  X  9"  timbers  are  suf 
ficient  ;  while  4"  X  12"  (in  each  half),  would  answer 
for  ab.  But  to  give  greater  transverse  stiffness  for 
supporting  floor  timbers,  it  is  preferred  to  have  the 
outside  course  of  lower  chord  timbers  5x12  inches. 


WOODEN  BRIDGES.  309 


310 


BRIDGE  BUILDING. 


The  piece  bj  having  no  office  but  to  fill  the  space  at 
b9  and  to  give  support  to  a  i,  may  be  of  any  convenient 
dimensions. 

The  maximum  tension  of  other  portions  of  the  lower 
chord  is,  for  be,  56,250;  for  cd,  81,250,  and  for  de, 
93,750Ebs.  For  the  upper  chord,  we  have  compression 
ofih,  hg  and  gf,  62,509ft>s.,  87,500ft>.,  and  100,OOOR>s.  re 
spectively. 

The  diagonals  and  verticals  are  liable  to  maximum 
tension  and  compression  as  shown  in  the  following 
statement ;  and  may  properly  be  of  dimensions  as 
marked  opposite  each  in  the  right  hand  column  below  ; 
in  case  of  double  members,  the  figures  indicate  the 
width  and  thickness  of  each. 


Parts. 

Tension,  Ibs. 

Compression,  libs. 

Cross-Section,  inches. 

bi 

28,000 

double  3  X  11 

d 

28,140 

single  5  X  12 

dh 

20,435 

"      4  x  12 

e9 

12,730 

,670 

"      3  x  11 

fd 

6,700 

6,700  ' 

d.     3x    6 

yc 

670 

12,730 

"      3x6 

hb 

20,425 

"    3}  x    7 

fa 

65,660 

"      8x9 

The  inside  course  of  lower  chord  timbers  may  be  — 
a  4"  x  12"  piece  extending  from  d  across  the  two  mid 
dle  panels  of  the  truss,  spliced  at  each  end  to  a  taper 
ing  piece  4  X  12  at  d,  and  2  X  12  at  b ;  and  consequently, 
3  X  12  at  c.  Then,  leaving  a  space  of  8"  between  half 
chords  at  d  and  e,  we  have  10"  at  c,  and  12"  at  b. 

Each  half  of  the  upper  chord  should  be  8"  x  12",  in 
the  two  middle  panels,  and  placed  9"  apart ;  connect 
ing  with  a  tapering  piece  each  way,  from  8  x  12  at  gy 


WOODEN  BHIDGES.  311 

to  6  x  12  at  i\  where  the  end  should  be  beveled  to  a 
line  bisecting  the  angle  aih,  and  abut  against  a  beveled 
shoulder  upon  the  upper  end  of  the  king  brace  ai. 
The  king  brace  is  also  cut  away  upon  the  inside,  leav 
ing  only  1"  in  thickness,  to  make  up,  with  bi  and  z'c,  a 
thickness  equal  to  the  space  (13")  between  the  half- 
chords  at  i. 

The  parts  thus  meeting  at  i  are  to  be  fastened  by  2 
transverse  bolts  of  at  least  2J"  in  diameter.  These 
afford  the  requisite  square  inch  of  bearing  surface  for 
each  IjOOOfos.  of  pressure,  with  an  unimportant  de 
ficiency  for  the  member  zc,  which  may  be  eked  out  with 
a  V  pin  through  bi  and  ic  only,  if  thought  advisable, 
thus  giving  55  square  inches  for  vertical  and  diagonal 
together. 

These  members  should  extend  at  least  14"  beyond 
the  centres  of  holes. 

At  h  and  <;,  the  three  diagonal  pieces  just  fill  the 
space  between  chord  timbers,  and  require  at  A,  two 
bolts  and  one  plain  pin  of  If "  in  diameter,  and  at  g, 
the  same  number  &c.,  of  If"  diameter.  The  diagram 
shows  only  two  bolts  at  each  connection. 

At  the  point  /",  where  two  pairs  of  braces  meet,  one 
pair  may  be  cut  off  at  the  meeting,  and  a  4  by  6  inch 
piece  introduced,  lapping  2  feet  between  the  cut  pieces 
(reduced  each  J  inch  in  thickness,  inside,  to  the  extent 
of  the  lap),  and  secured  by  2  bolts  and  1  pin  of  V 
diameter;  the  upper  end  passing  between  the  opposite 
braces,  the  latter  being  boxed  J"  inside,  to  afford  room 
for  the  4"  piece ;  and  the  whole  secured  by  a  single 
1J"  or  1 J"  bolt  through  chord  and  braces. 

The  connections  at  the  lower  chord  are  somewhat 
more  complicated,  but  involve  little  difficulty.  The 
best  connection  at  a,  is  made  by  cutting  a  vertical 


312  BRIDGE  BUILDING. 

shoulder  or  heading  J"  deep,  upon  both  sides  of  the 
half  chord,  as  shown  by  the  vertical  dotted  line  in  the 
diagram  A,  Fig.  66;  the  brace  being  forked  with 
counter  shoulders  upon  the  inside.  This  affords  36 
square  inches  of  shoulder  surface,  which,  assisted  by  2 
bolts  of  V  diameter,  give  50  square  inches,  to  with 
stand  less  than  44,0001bs.  The  end  of  the  brace  is 
thus  made  to  bear  directly  upon  the  abutment  without 
any  crushing  action  upon  the  chord. 

At  6,  the  space  in  the  chord  is  12",  while  the  verti 
cals  descending  parallel,  would  occupy  11".  But  giv 
ing  a  divergence  of  2J",  and  boxing  f  "  upon  the  inside 
of  chord  timbers,  leaves  a  space  of  6J"  between  verti 
cals  at  b.  Then,  boxing  bh  J"  upon  the  inside  at  the 
crossing  with  ic9  there  will  be  a  3"  space  between 
braces  bh  at  6,  and  a  thickness  of  4 J"  (of  the  pieces  bh) 
between  the  verticals  bi;  also,  a  shoulder  of  1J"  upon 
the  outside,  which  may  be  made  to  act  vertically  in  a 
boxing  upon  the  inside  of  fo',  thus  securing  the  requi 
site  bearing  surface  for  the  thrust  of  bh.  Thus  ar 
ranged,  the  point  should  be  fastened  with  2  bolts  and 
1  pin  of  If"  diameter. 

The  piece  bj  will  have  3"  in  thickness  at  6,  and  will 
be  furred  out,  if  necessary,  to  fill  the  space  atj. 

The  space  at  c  is  10" ;  and,  eg  being  shouldered  |" 
at  the  upper  side  of  the  chord  at  c,  and  boxed  J"  at  the 
crossing  with  hdt  the  point  c  may  be  secured  by  2 
bolts  and  1  pin  of  1 J"  or  2"  diameter. 

A  J"  boxing  of  df  at  rf,  upon  the  inside,  leaves  a 
thickness  of  9",  being  1"  greater  than  the  space  in  the 
chord,  and  the  pieces  (//"therefore  require  a  further  re 
duction  in  thickness  upon  the  outside  between  chord 
timbers,  of  J"  upon  each.  The  point  d,  requires  If" 
bolts  and  pin. 


WOODEN  BRIDGES. 

The   two   single   diagonals   meeting   at  e,  may   be 
halved  into  one  another  at  the  crossing,  and  a  3x11  inch 
piece  lapped  and  locked  on  to  each,  as  shown 
Fid.  67.    by  a  a  in  Fig.67  ;  thus  serving  to  fill  the  space 
in  the  chord,  and  to  restore  strength  to  the 
diagonals.     The  lap  pieces  are  to  be  reduced 
3*        to  2J"  in   thickness   below   the   lock   at   I. 


ra 


Two  1 J''  bolts  are  sufficient  at  the  point  e. 

Transverse  joists,  or  floor  beams  may 
be  placed  upon,  or  suspended  below  either 
the  lower  or  upper  chords.  Sway  bracing 
may  be  locked  and  bolted  upon  the  upper 
chords,  and  iron  X  tie  rods  used  at  the  lower 
chords ;  the  beam  timbers  being  shouldered 
against  the  inside  of  cords,  so  as  to  strut 
them  apart  against  the  action  of  the  ties. 

Angle  braces  from  the  king  brace  ai9  to  a  transverse 
beam  from  truss  to  truss  at  i,  will  aid  in  preserving  the 
erect  position  of  trusses.  These  braces  should  usually 
be  lapped  and  bolted  at  the  ends,  so  as  to  act  by  either 
tension  or  thrust 

The  preceding  specifications,  it  is  hoped,  will  serve 
to  make  the  peculiarities  of  detail  in  the  kind  of  truss 
under  consideration,  properly  understood.  It  may  be 
deemed  advisable  to  adopt  the  rectangular,  instead  of 
the  Trapezoidal  form  of  outline  for  the  truss,  by  extend 
ing  the  upper,  to  the  same  length  with  the  lower  chord, 
inserting  vertical  posts  at  the  ends,  and  exchanging  the 
double  vertical  bi,  to  a  single  diagonal  meeting  the  up 
per  chord  and  end  post  at  their  point  of  junction  ;  thus 
simplifying  the  connections  at  b  and  i. 

This  modification,  unlike  the  case  of  the  trapezoidw^A 
verticals,  involves  no  increase  in  amount  of  action  upon 
materials,  though  it  increases  the  number  of  members, 
and  changes  the  manner  of  distribution  of  the  action. 


314  BRIDGE  BUILDING. 

MODULUS  OF  STRENGTH,  FOR  BRIDGE 
TRUSSES. 

It  is  shown  in  preceding  pages  of  this  work,  that, 
knowing  by  experiment  the  strength  of  the  materials 
to  be  employed,  we  may  calculate  the  necessary  cross- 
section  of  each  part  of  a  bridge  truss,  in  order  that  it 
may  sustain  a  given  load,  with  a  given  stress  upon  the 
materials. 

It  is  sometimes,  however,  a  satisfaction  to  have  a 
confirmation  of  the  correctness  of  our  calculations,  by 
direct  experiment  upon  the  same  combination  com 
plete,  which  we  propose  to  employ  for  actual  use.  For 
this  purpose,  instead  of  applying  the  test  to  a  full  sized 
structure,  which  would  involve  a  great  deal  of  labor 
and  expense,  the  test  may  be  applied  to  a  model,  made 
in  the  true  proportions,  upon  any  scale. 

Now,  it  is  obvious  that  with  the  same  combination 
and  arrangement  of  members,  the  stresses,  whether 
positive,  negative  or  transverse,  produced  upon  the 
several  parts  by  the  acting  forces,  will  be  in  proportion, 
throughout,  to  the  weight  sustained,  whatever  be 
the  length  of  pieces  ;  such  stresses  being  determined  by 
the  positions  and  angles,  and  not  by  the  lengths  of 
pieces. 

It  is  further  manifest  that  the  ability  of  parts  to 
withstand  the  effects  of  the  acting  forces,  must  be  as 
the  cross-sections  of  parts  respectively ;  and  in  similar 
models,  the  parts,  being  similar  solid  figures,  have  their 
cross-sections  as  the  squares  of  the  magnitude  of  scale 
upon  which  they  are  respectively  constructed,  while 
the  bulk  and  weight  of  each  corresponding  part,  and 
of  the  combinations  complete,  are  as  the  cubes  of  the 
magnitude  of  scale. 


MODULUS  OF  STRENGTH.  315 

Then,  assuming  two  similar  models,  the  scale  of  one 
being  m  times  as  great  as  that  of  the  other,  the  weights 
which  they  will  respectively  bear,  under  the  same 
stress  of  material,  will  be  as  W  to  Wm2,  while  their  re 
spective  weights  will  be  as  1  to  m3. 

Now,  dividing  the  sustaining  power  of  each  by  its 

own  weight,the  quotients  are  as  "W  toW  — -3  or  as  W  to 
— .  But  the  lengths  being  as  L  to  Lm,  if  we  multiply 

the  quotients  just  found  by  respective  lengths,  we  have 
WL  for  the  one,  and  Lm  W  -f-  m,  =  WL  for  the  other ; 
showing  that  the  length  of  a  model  truss  by  the  num 
ber  of  times  its  own  weight  which  it  can  bear  (with  a 
given  stress),  is  a  constant  quantity,  whatever  be  the 
scale  of  such  model. 

Again,  the  quotients  W,  and  — ,   multiplied  by  the 

lengths  L  and  Lm,  give  the  products  WL,  and  --  X  Lm, 

equal  to  WL.  Hence,  the  product  of  a  truss  medal  into 
the  number  of  times  its  own  weight  which  it  is  able 
to  sustain,  is  also  constant,  whatever  be  the  relative 
values  of  the  two  factors. 

It  follows,  that  making  these  two  factors  variable, 
and  representing  them  by  Q  and  L,  the  one  increases 
at  the  same  rate  at  which  the  other  is  diminished  ;  and, 
when  Q  =  1,  L  must  be  equal  to  the  greatest  length 
at  which  a  truss  of  the  same  plan  and  proportions,  and 
under  the  same  stress  of  materials,  can  sustain  its  own 
weight  alone. 

This  length,  as  we  have  seen,  is  determined  for  a 
model  upon  any  plan,, constructed  upon  whatever  scale, 
by  multiplying  the  length  of  model  by  the  number  of 
times  its  own  weight  it  is  capable  of  sustaining. 


316  BRIDGE  BUILDING. 

This  product  may  be  called  the  MODULUS  OF  STRENGTH, 
and  the  plan  of  truss  which  gives  the  largest  MODULUS, 
may  fairly  be  regarded  as  the  strongest  plan. 

The  Modulus  may  refer  either  to  the  actual  break 
ing  load,  as  found  by  experiment,  or  to  the  load  pro 
ducing  given  rates  of  strain  upon  materials,  as 
determined  by  calculation. 

EXAMPLES. 

(1).  A  bar  of  cast  iron  1  inch  square  and  12"  between 
supports,  will  bear  (at  6,000rbs.  to  the  inch  of  section, 
upon  a  leverage  equal  to  depth  of  beam),  a  distributed 
load  of  4,000116s.  which  divided  by  its  weight,  =  say 
3.12ft)s.  gives  Q  =  1250  ;  and  L  being  1  foot,  the  Modu 
lus  =  QL,  =  1,250  feet. 

(2).  A  beam  of  pine  timber  12'  long  and  6"  square, 
at  l,500flbs.  to  the  inch  upon  a  leverage  equal  to  depth, 
as  above,  bears  a  distributed  load  of  18,0001bs.  [CXLIL] 
For  the  weight,  say  3  cubic  feet  at  36ft>s.  =  108ft>s. ; 

1ft  000 

whence,  Q  =  ^  =  166.6,  which  multiplied  by  L 
(=  12')  gives  Modulus  equal  to  2,000  ft. 

By  reducing  the  length  of  the  beam  just  considered, 
to  6  feet  in  length,  retaining  the  same  section,  it  would 
give  a  Modulus  of  4,000  feet,  instead  of  5,000,  as  given 
in  the  Appendix  to  my  former  work ;  the  difference 
arising  from  the  assumption  of  a  smaller  specific 
gravity  for  pine  in  the  latter  case. 

(3).  The  two  panel  model  with  chord  and  rafter 
braces,  mentioned  in  the  latter  part  of  §  [CLVIII],  20" 
long,  and  weighing  0.18rb.  supported  a  load  equiva 
lent  to  3,885  times  its  weight,  while  L  =  1§  feet ; 
whence,  3,885 xlf  =  6,475  feet,  =  its  Modulus. 


MODULUS  OF  STRENGTH.  317 

(4).  A  model  wooden  truss  4  feet  long,  made  many 
years  ago  by  the  author,  on  the  plan  of  the  truss  Fig. 
66,  having  10  panels,  and  a  depth  equal  to  j\  of  its 
length,  weighed  0.9Ibs,  and  bore  a  distributed  load  of 

6001bs.  Hence,  the  modulus  of  the  truss  was  —  X  4 
=  2,664  feet,  being  more  than  half  a  mile. 

The  model  was  somewhat  strained  but  not  broken ; 
and  recovered  its  normal  shape  and  condition  on  re 
moval  of  the  load.  It  was  subsequently  sent  to  the 
U.  S.  Patent  Office. 

These  examples,  however  can  not  be  taken  as  in 
dices  to  the  relative  merits  for  general  use,  of  the 
different  forms  of  truss  to  which  they  refer.  Each 
possesses  qualities  suited  to  special  occasions. 

(5).  A  model  of  a  6  feet  Trapezoidal  Iron  Truss  (the 
first  ever  constructed],  weight  a  little  less  than  three 
pounds,  sustained  TOOSbs.  distributed,  without  any  ap 
pearance  of  overstraining ;  thus  showing  a  modulus  of 

12?  x  6  =  1,400  feet,  with  an  estimated  stress  upon  the 

chord,  at  the  rate  of  about  16,OOOIbs.  to  the  square 
inch.  The  model  represents  a  truss  of  144  feet,  upon 
a  scale  of  J  inch  to  the  foot.  The  sustaining  power  of 
a  full  sized  truss  in  the  same  proportions,  would  be 
700  x  242,  =  403,200ft)s,  while  the  weight  of  truss  would 
equal  3  X  243  =  41,472ft>s.  Doubling  this  for  two 
trusses,  and  adding,  say  10,0001bs,  for  beams,  &c.,  we 
have  92,944ft)s.  for  the  weight  of  a  144  feet  bridge, 
capable  of  sustaining,  at  a  stress  of  16,000ft>s.  to  the 
square  inch  upon  the  chords,  over  356  net  tons  beside 
weight  of  structure. 


DRAWBRIDGES. 

CLXY.  The  present  is  undoubtedly  distinguishable 
from  all  preceding  periods  of  history,  by  the  increased 
amount  of  locomotion,  both  of  persons  and  property, 
which  takes  place  both  by  land  and  water.  Hence, 
the  frequent  crossing  of  one  another  by  land  and  water 
lines  of  transit,  as  well  as  the  crossing  by  the  former 
of  unnavigable  waters,  and  of  streets  and  ravinesy 
creates  a  large  demand  for  the  construction  of  BRIDGES  ; 
which  forms  the  special  subject  of  the  present  volume. 

Furthermore,  as  convenience  often  requires  that 
these  intersecting  lines  by  land  and  water  should  oc 
cupy  so  nearly  the  same  elevation  that  both  can  not  be 
used  at  the  same  moment,  a  necessity  arises  for  the 
frequent  construction  of  DRAW  BRIDGES,  which  may  be 
temporarily  withdrawn  from  over  the  water  highway 
during  the  passage  of  water  craft,  and  replaced  for  the 
transit  of  laud  vehicles. 

Cases  requiring  the  construction  of  draw  bridges 
occur  so  frequently  at  the  present  day,  that  a  treatise 
upon  bridge  construction  may  be  considered  somewhat 
incomplete,  which  does  not  embrace  the  construction 
of  Draw  Bridges,  as  well  as  stationary  structures. 

The  subject  of  Draw  Bridges  having  been  omitted 
m  the  preceding  edition  of  this  work,  it  has  come  to 
the  knowledge  of  the  author  that  such  omission  has 
occasioned  disappointment  to  some  who  have  made 
use  of  the  book.  In  consideration  of  this,  as  well  as 
the  fact  that  the  author  has  originated  some  plans  and 
devices  which  he  believes  to  be  valuable  and  useful  in 


320  BRIDGE  BUILDING. 

the  construction  of  draw  bridges,  the  current  chapter 
is  introduced  in  the  present  edition,  in  order  to  make 
the  work  as  satisfactory  and  useful  as  may  be  to  those 
who  may  have  occasion  to  consult  its  pages. 

The  present  design  is  not  a  historical  sketch  of  the 
construction  of  draw  bridges,  but  to  give  the  author's 
views,  derived  from  experience,  obserration  and  in 
vestigation,  as  to  the  most  direct,  feasible,  and  conven 
ient  means  of  accomplishing  the  ends  requiring  the  use 
-of  such  works. 

CLXVI.  The  indispensable  requisites  of  a  draw 
'bridge  are,  first,  strength  to  sustain  with  safety  the 
weight  of  the  land  traffic,  and  second,  mobility,  ena 
bling  it  to  be  withdrawn,  so  as  to  afford  sufficient  width 
of  unobstructed  water  way,  and  sufficient  head  room 
for  the  passage  of  the  water  traffic.  Hence,  strength 
•combined  with  lightness  is  a  desideratum. 

Draw  bridges,  as  hitherto  constructed  and  used, 
may  be  distinguished  into  three  classes;  Retractile, 
Swing  (or  pivot),  and  Lift  Draw  Bridges.  The  former 

FIG.  68. 


are  withdrawn  bodily,  either  in  the  direct  line  of  the 
land  traffic,  or  obliquely,  so  as  not  to  come  in  conflict 
with  the  stationary  portion  of  the  way  ;  as  represented 


DRAW  BRIDGES. 


321 


in  Fig.  68,  where  CO  shows  the  water  channel,  DD,  the 
draw  closed,  and  D'D',  the  draw  open. 

In  case  of  direct  retraction,  the  draw  must  either  oc 
cupy  a  higher  position  than  the  permanent  way,  so  as 
to  be  drawn  back  over  a  portion  of  it,  and  the  two 
planes  connected  by  an  inclined  apron  (a  plan  not 
feasible  for  rail  roads),  or  a  portion,  a  (Fig.  69),  of  the 
way  at  the  heal  of  the  draw  proper,  Z),  withdrawn  late 
rally,  as  to  the  position  of  #',  to  make  room  for  the 
longitudinal  withdrawal  of  the  draw  proper. 

FIG.  69. 

1 


a 

D 

a' 

1 

These  movements  are  effected  by  having  the  mova 
ble  bodies  mounted  upon  wheels  or  rollers,  running 
upon  hard  level  ways,  so  as  to  reduce  the  amount  of 
friction,  and  consequently  that  of  the  required  motive 
power,  to  a  minimum. 

But  retractile  draws,  though  they  may  be  still  used 
in  a  few  cases,  and  under  peculiar  circumstances,  must 
be  regarded  as  nearly  obsolete,  having  been  mostly 
superseded  by  the  swing  draw,  which  has  important 
advantages  in  convenience  of  construction  and  opera 
tion.  No  practical  details,  therefore,  as  to  the  con 
struction  of  retractile  draws,  will  be  given  at  this 
time,  as  such  details  if  given,  would  be  almost  certain 
never  to  be  adopted  in  practice. 

CLXYII.  The  Swing  or  Pivot  draw  is  either  mounted 
upon  a  pivot  P  (Fig.  70),  in  the  vertical  line  through 
41 


322 


BRIDGE  BUILDING. 


its  centre  of  gravity,  or  upon  wheels  or  rollers  running 
upon  a  horizontal  circular  way  or  track  tt,  with  its 
centre  in  said  vertical  line  ;  or  what  is  more  common, 
the  weight  is  divided  between  a  central  pivot  and  the 
track  and  rollers. 

FIG.  70. 


ft 


It  will  be  seen  that  by  this  arrangement,  the  draw 
has  only  to  be  gyrated  through  a  quadrant,  to  bring  it 
to  a  position  parallel  with  the  side  of  the  navigable 
channel  (7,  and  leave  the  latter  unobstructed.  It  is  also 
obvious  that  the  draw  having  its  centre  of  gravity  at  P, 
the  moments  (with  respect  to  P),  of  the  portions  or 
arms  on  opposite  sides  of  P,  must  be  equal,  whatever 
be  the  relative  lengths  of  those  portions;  whence,  in 
general,  the  length  of  arm  spanning  the  water  channel 
being  given,  the  shorter  the  other  arm,  the  greater 
must  be  its  weight,  though  the  exact  proportion  will 
depend  upon  the  disposition  of  material,  whether  near 
or  remote  from  P. 

It  follows  that  it  is  usually  little  if  any  more  expen- 


DRAW  BRIDGES.  32S 

sivc  to  constructor  work  a  draw  with  two  equal  arms, 
and  covering  two  equal  water  channels  (which  is  often 
highly  advantageous),  than  one  having  one  short  arm, 
with  extra  weight  as  a  counterpoise  to  the  long  arm. 
This  is  not  the  case  as  to  the  retractile  draw,  which 
shows  one  advantage  in  favor  of  the  pivot  draw. 

Equal  arms  also  serve  to  balance  the  action  of  wind 
upon  the  pivot  draw,  which  often  effects  a  serious 
drawback  to  the  convenient  working  of  the  swing 
bridge,  and  this  would  seem  to  give  some  advantage 
to  the  .retractile  draw,  over  the  swin<?  draw  with  une- 

O 

qual  arms. 

The  portion  extending  over  the  water  channel,  in 
both  the  retractile  and  the  swing  draw,  require  the 
same  weight  of  material,  and  the  same  counterpoise 
toward  the  opposite  end.  Consequently,  the  weight 
to  be  moved  in  working  the  draw,  requires  to  be  about 
the  same  in  both.  But  the  retractile  is  to  be  moved 
bodily,  and  if  withdrawn  obliquely  at  45°  with  its 
longitudinal  axis,  must  move  through  a  space  equal  to 
the  width  of  channel  multiplied  by  \/2.  If  withdrawn 
in  the  direct  line  of  its  length,  it  moves  over  the  width 
of  channel,  in  addition  to  the  movement  required  for 
the  displacement  of  the  section  of  road  (a.  a',  F.  69), 
equal  in  length  to  said  width  of  channel,  making  an 
amount  of  movement  about  equal  to  that  required  in 
ease  of  the  oblique  withdrawal.  * 

The  swing  draw,  gyrating  about  its  centre  of  gravity, 
the  amount  of  movement  equals  twice  the  weight  of 
the  long  arm  (the  one  spanning  the  water  channel), 
moving  through  the  quadrant  of  a  circle  with  a  radius 
equal  to  the  distance  of  the  centre  of  gravity  of  said 
long  arm,  from  the  centre  of  motion  ;  which  distance 
is  about  55  per  cent,  of  the  width  of  channel,  allowing 


324  BRIDGE  BUILDING. 

for  the  distance  of  the  centre  of  motion  back  from  the 
water's  edge.  The  length  of  the  quadrant  equals 
about  1.57  Rad.,  and,  denoting  the  width  of  channel  by 
C,  and  substituting  0.55C  for  Rad.,  we  have  1.57  x 
.550  X  2vvt.  of  long  half  of  draw,  =  quantity  of  move 
ment,  ==  0.8635C  x  wt.  of  draw  ;  assuming  the  weight 
of  draw  to  be  equal  to  twice  the  weight  of  the  long 
half.  If  the  short  arm  be  heavier  than  the  other,  the 
space  traversed  by  its  centre  of  gravity  is  less  in  like 
proportion. 

Hence,  the  quantity  of  movement  in  working  the 
retractile  draw,  is  to  .that  of  working  the  swing 
draw,  about  as  CV2  to  0.8635C;  being  some  63 
per  cent,  greater  for  the  former  than  for  the  latter. 
The  difference  in  the  required  power  for  working  the 
draws  respectively,  may  be  assumed  to  be  about  the 
same,  as  the  appliances  for  effecting  the  movement 
have  about  equal  advantages,  and  the  resistance  to  mo 
tion  is  about  the  same  in  the  two  cases. 

This  decided  advantage  in  favor  of  the  swing  draw, 
with  no  apparent  offset  in  favor  of  the  retractile,  is 
sufficient  to  account  for  the  prevalent  discardment  of 
the  latter,  and  adoption  of  the  former ;  as  well  as  for 
its  being  here  referred  to  as  an  obsolete  device. 

CLXVTH.  The  truss  work  of  the  swing  draw  when 
in  motion,  being  entirely  supported  by  the  pivot  at  the 
centre  of  motion,  and  the  wheels  or  rollers  a  few  feet 
therefrom,  obviously  suffers  a  reversed  action  in  the 
upper  and  lower  members,  from  what  they  would 
suffer  if  supported  at  the  ends.  That  is,  in  the  former 
case,  the  upper  members  are  exposed  to  tension,  and 
the  lower,  to  compression,  instead  of  the  reverse, 
which  takes  place  in  the  latter  case. 


SWING  DRAW  BRIDGES. 


325 


Two  plans  have  been  employed  for  meeting  these 
conditions  ;  one  of  which  is  the  use  of  parallel  chord 
trusses,  with  the  upper  chord  to  sustain  tension  with 
occasional  compression  upon  the  end  portions,  and  the 
lower  chord  to  sustain  compression,  with  occasional 
tension  upon  parts  toward  the  ends. 

CLXIX.  The  other  plan  is,  the  construction  of 
trusses  (ab  Fig.  71),  from  the  turn  table  T,  to  either  end, 
acting  upon  one  another  by  compression  at  the  lower 
chord  through  or  over  the  turn  table,  and  sustained  at 
the  outer  ends  by  oblique  suspension  rods  or  cables, 
eb  and/d,  descending  from  tower  frames  erected  over 
the  turn  table. 

FIG.  71. 


XX 


\\xxxx 


The  trusses  may  be  constructed  upon  any  plan  suita 
ble  for  a  stationary  bridge  of  like  span.  But  the  lower 
chord  must  be  capable  of  sustaining  compressive  action 
in  the  direction  of  its  length,  equal  to  the  excess  of 
horizontal  force  of  suspension  rods  eb  and  fd,  over  the 
tension  of  respective  parts  of  said  lower  chord,  due  to 
weight  of  structure. 

The  horizontal  action  of  eb,  equals  half  the  weight 

of  the  long  arm  ab,  multiplied  by  *&,  and  it  is  advisable 
that  the  chord  gb  be  able  to  sustain  that  amount  of 


326  BRIDGE  BUILDING. 

compression  throughout,  though  some  deduction  may 
be  made  in  the  central  portion  in  case  economy  can  be 
promoted  thereby,  as  perhaps  may  not  be  the  case  to 
any  considerable  extent. 

The  lower  chord  gb,  is  relieved  of  tension  through 
out  its  whole  length  by  the  action  of  eb,  which  must 
continue  nearly  or  quite  at  its  maximum  while  loads 
are  in  transit,  as  the  end  b  will  seldom  be  raised  when 
unloaded,  so  as  to  relieve  eb  to  any  considerable  extent ; 
while  the  tendency  of  load  to  elongate  the  lower  chord, 
will  also  tend  to  increase  the  tension  eb,  and  may  in 
crease  it  considerably  beyond  what  it  endures  from 
simply  sustaining  half  the  weight  of  the  truss.  But 
this  point  can  not  be  precisely  determined. 

These  facts  may  properly  be  considered  in  propor 
tioning  the  lower  chord ;  but  the  matter  should  be 
handled  with  caution,  and  with  a  constant  leaning  to 
the  side  of  safety,  in  case  of  any  uncertainty  in  regard 
to  the  amount  and  kind  of  stress  upon  the  various 
parts. 

In  case  of  unequal  arms,  as  represented  in  the  Figure, 
the  short  arm  will  generally  require  a  greater  weight 
to  be  thrown  upon  the  king  post  fh  than  upon  eg,  upon 
which  two  (regarding  at  present  only  one  side  of  the 
bridge),  the  weight  of  superstructure  is  concentrated. 
It  therefore  becomes  necessary,  in  order  to  a  uniform 
distribution  of  weight  upon  the  turn  table,  that  a  por 
tion  of  this  excess  be  transferred  from  fh  to  eg,  through 
the  tension  of  ce  and  ha,  or  by  equivalent  means.  But 
assuming  that  the  reader  is  versed  in  the  general  modes 
of  calculating  strains,  as  explained  and  illustrated  in 
this  and  other  works  treating  of  the  subject,  I  shall 
not  go  much  into  detail  in  that  branch  of  the  matter 
in  hand,  at  this  time. 


SWING  DRAW  BRIDGES.  827 

The  trusses  being  constructed  upon  any  approved 
plau  from  turn  table  to  adjacent  abutments  or  piers, 
and  proportioned  as  for  stationary  bridge  spans,  with 
the  exception  of  the  rigid  lower  chord  as  above  re 
ferred  to,  extending  across  the  turn  table;  and  the 
tower  frame  erected,  the  rod  or  cable  eb  must  have  sec 
tion  sufficient  to  bear  a  tension  equal  at  least  to  half 
the  weight  of  the  arm  ab,  multiplied  by  — .  The  rod 
fd  will  have  tension  determined  by  the  disposition  and 
amount  of  ballast  upon  the  arm  cd,  as  well  as  the 
weight  of  the  arm  cd  itself.  The  tension  of  fd  will 
generally  exert  less  horizontal  action  than  eb,  and  the 
deficiency  of  horizontal  action  must  be  made  up  by 
the  horizontal  action  of  ec  and  ah,  in  order  to  brinsc 

'  O 

the  centre  of  pressure  over  the  centre  of  the  table. 
The  horizontal  action  of  ef  (equal  to  its  full  tension), 
must  be  equal  to  that  of  eb,  less  that  of  ec  ;  or,  equal  to 
the  horizontal  action  of  fd. 

But  these  several  stresses  are  easy  of  calculation  by 
modes,  it  is  believed,  clearly  explained  in  the  present 
work,  and  from  such  calculations  the  following  results 
are  readily  obtained. 

CLXX.  Representing  the  constant  panel  weight  of 
the  arm  ab  by  wf,  the  maximum  variable  panel  load  by 
w,  and  w+wf  by  W,  as  usual  in  this  work ;  also,  making 
r  =  ag,  —  ae,  and  h  =  horizontal  panel  width,  we  have 
the  horizontal  action  of  eb  equal  to  5?//x -^-,=2510'^  . 

The  stress  of  gb  due  to  a  maximum  gross  load,  in  the 
two  middle  panels,  equals  11W-.  That  in  the  next 

panel  each  way,  =  9W-?,  and  in  the  next,  6JW-S  while 
the  stress  of  the  two  remaining  panels  on  the  right, 
equals  4JW-*,  and  on  the  left  2VW~,  and  zero,  respect- 


328  BRIDGE  BUILDING. 

ively.  Then,  assuming  W  =  4iv',  the  stresses  of  res 
pective  portions  of  lower  chord  due  to  a  max.  gross 
load,  in  terms  of  iof,  equal  w'7^  with  the  coefficients 
44,  36,  26,  18,  10  and  0;  showing  that  the  tension  of 
eb  counteracts  over  J  the  tendency  toward  tension  on 
lower  chord,  as  to  the  two  middle  panels,  over  f  as  to 
the  two  next  panels,  and  substantially  the  whole,  as  to 
the  remaining  parts  of  said  chord,  in  a  structure  ar 
ranged  as  in  Fig.  71,  and  with  w  =  3w'. 

On  the  other  hand,  the  minimum  tendency  to  ten 
sion  on  the  two  middle  panel  lengths  of  lower  chord, 

is  HM;'— .  Hence  the  compression  of  25w/—  upon  those 
parts,  due  to  the  horizontal  action  of  eb,  is  reduced  (by 
such  tendency  to  tension),  to  (25-ll)i0r— ,  = 


and,  to  (25-9)  ?/;'-,=16w/-  upon  succeeding  panel- 
lengths,  either  way,  while  for  succeeding  panel-lengths 
toward  6,  the  coefficients  of  w'-^  are  18 J,  20J  and  20J, 
and  for  those  toward  g,  18J,  22J  and  25.  * 

The  maximum  thrust  and  tension  for  successive  por 
tions  of  the  lower  chord,  beginning  at  the  turn  table, 
are,  for  part  over  turn  table,  and  first  panel-length  from 

Om  Comp.  25?(/—  Tension  0 

2d  panel,  "       22 J-  "  "       0 

3d  and  8th         "       18J  "  "       lw'-% 

4th  "     7th         "       16J  "  "      11  " 

5th  "     6th         "       14    "  "      19  " 

9th  "  10th        "       20J  "  "       0  " 

The  other  members  of  the  truss  ab  are  subject  to  the 
same  stresses  as  if  it  were  a  stationary  bridge  truss; 
and,  if  the  structure  have  equal  arms,  the  stresses  upon 
members  of  the  opposite  arm,  will  of  course  be  the 
same  as  upon  corresponding  members  of  the  arm  ab. 


SWING  DRAW  BRIDGES. 

CLXXI.  If  cd  have  half  the  length  of  ab,  its  weight 
will  balance  the  half  (gC),  of  ab  next  the  turn  table,. 
while  the  half  Cb  must  be  counterpoised  by  extra  weight 
upon  cd,  having  moment  equal  to  that  of  Cb,  with  res 
pect  to  a  transverse  axis  through  the  centre  of  motion  ; 
and  the  stress  of  fd  will  be  determined  by  its  length, 
and  the  weight  sustained  by  it.  In  case  the  extra 
weight  be  uniformly  disposed  upon  the  two  outer  pan 
els,  J  of  it,  together  with  J  the  weight  of  the  arm  cd, 
(=  2Jw/),  must  be  sustained  by  c/f,  and  the  weight  of 

ballast  will  be  5wf  x  7ff  +  ffi,   j   of  which,   added  to 

4/4  -f   fa™      ° 


2J?*/,  equals  the  weight  sustained  by  fd,  whence  we 
obtain  the  tension  of  fd,  its  horizontal  action,  and  the 
complementary  horizontal  action  of  ce,  required  to  ba 
lance  that  of  cb. 

In  this  case,  the  members  meeting  at  the  points  e 
and/,  should  have  unyielding  connections  by  pins  and 
eyes,  or  screws  and  nuts.  But  in  case  of  equal  arms, 
dfeb  may  be  continuous  cables  (usually  one  on  each 
side  of  each  truss),  attached  at  b  and  d,  and  acting  by 
simple  pressure  at  e  and  /,  those  points  being  strutted 
apart  by  a  force  equal  to  SM?'  (=*  vertical  pressure  at  e), 

x  ^.     The  piece  ac  should  have  loose  connections  at 

the  ends  (so  as  to  act  by  thrust  only),  or  what  is  better, 
should  be  omitted  entirely,  and  the  single  pair  of  diag 
onals  inserted  as  indicated  by  the  dotted  lines  fg  and 
ch,  instead  of  shorter  ones,  ce,  etc.,  so  as  to  give  free 
and  independent  action  to  the  trusses  either  way,  by 
a  slight  springing  of  the  long  king  posts,  as  the  trusses 
are  deflected  by  load. 

The  tension  of  fd  modifies  that  due  to  the  chord  hdr 
on  the  same  principle  explained  with  regard  to  eb  and 
gb,  and  to  an  extent  determined  b}'  the  length  of  dhy 
42 


330 


BRIDGE  BUILDING. 


and  other  conditions,  and  which  can  not  be  expressed 
in  a  general  formula. 

CLXXII.  Proceeding  to  the  other  case  mentioned, 
and  which  may  be  illustrated  with  reference  to  Fig.  72, 
both  upper  and  lower  chords  require  to  be  so  con 
structed  as  to  be  able  to  act  both  by  tension  and  thrust, 
except  as  to  the  part  across  the  turn-table,  and  one, 
two,  or  three  panels  either  way  therefrom,  as  circum 
stances  may  require. 

FIG.  72. 


When  out  of  contact  with  the  abutment  at  I,  the 
diagonal  In  sustains  (using  the  accustomed  symbols), 
\w',  and  7co,  etc.  to  bx,  sustain  respectively  and  succes 
sively  wr  with  the  coefficients  1,  1},  2,  2J,  3,  3J,  4,  4-J 
and  5.  These  weights  determine  the  stresses  of  those 
members,  due  to  weight  of  structure  (and  also  show 
for  xy,  a  tension  of  50M?'-^,  including  the  horizontal 
action  of  xz,  if  any),  and  show  for  several  of  them 
toward  the  right,  their  maximum  stresses.  But  when 
the  end  I  touches  the  abutment,  and  is  in  position  for 
the  transit  of  loads,  and  weight  is  imposed  upon  any 
part  between  a  and  6,  the  materials  yielding  more  or 
less  in  consequence  of  elasticity,  a  portion  of  such 
weight  bears  at  £,  and  the  remainder  at  a. 

If  the  upper  chord  were  relaxed  between  x  and  ?/, 
the  respective  portions  of  weight  bearing  at  a  and  I 
could  be  readily  determined,  being  the  same  as  in  case 


SWING  DRAW  BRIDGES.  831 

of  an  ordinary  truss.  But  the  portion  of  chord  xy 
being  under  tension  equal  to  50w'—  ,  as  already  stated 
(regarding  the  abutment  as  sustaining  no  weight  of 
structure),  the  truss  must  act  in  the  manner  of  abeam 
continuous  over  one  support,  and  discontinuous  at  the 
next,  so  that,  when  loaded,  there  will  be  a  neutral 
point  where  the  action  upon  chords  changes  from  ten 
sion  to  thrust  and  the  contrary. 

Now  the  tension  of  :ry-|-hor.  action  of  xz,  equal  to 
oOw/—  ,  must  be  exhausted  by  the  hor.  ac.  of  bx,  ex  etc., 
before  any  compressive  action  can  take  place  upon  the 
upper  chord.  In  other  words,  diagonals  inclining  to 
the  left,  with  truss  fully  loaded  from  a  to  I,  must  exert 
a  hor.  action  at  the  upper  chord  greater  than  those 
inclining  to  the  right  (including  with  the  latter  the- 
hor.  thrust  of  /m),  by  50w'—  . 

Then,  assuming  all  the  weight  at  the  points  £,J,  /:, 
and  J  of  that  at  //,  to  bear  at  /,  and  all  at  the  six  points 
from  g  to  b  inclusive  (except  J  W  at  y\  to  bear  at  tf  , 
the  horizontal  action  toward  the  left  upon  the  upper 
chord,  equals  IW-  ;  and  that  toward  the  left, 


the  difference  being  12JW—  ';  and  if  W  =  4w',  then 
12JW  =  50i#  ',  showing  that  the  action  toward  the  right, 
upon  the  upper  chord,  is  just  equal  to  that  toward  the 
left,  including  in  the  latter,  the  action  of  xy  and  xz» 
Hence  it  will  be  seen  that  under  the  conditions  here 
assumed,  the  horizontal  action  of  m?,  mj,  mi  and  ng,  is 
just  equal  to  that  of  gr,  fs  and  et  in  the  opposite  direc 
tion,  and  consequently,  tm  alone  of  the  upper  chord  is 
subject  to  compression,  and  el  alone  of  the  lower  chord,. 
subject  to  tension,  while  dc  and  ut  are  neutral  ;  ad  al 
ways  under  compression,  and  wj  always  under  tension  ; 
since  this  condition  of  load  obviously  throws  a  greater 


332  BRIDGE  BUILDING. 

bearing  at  I  than  can  occur  when  the  opposite  arm  is 
wholly  or  partially  loaded,  so  as  to  bring  greater  ten 
sion  upon  xy,  and  exert  greater  counterpoise  action 
upon  the  arm  al.  Hence  this  condition  gives  the  max 
imum  compression  upon  the  upper,  and  the  maximum 
tension  upon  the  lower  chord. 

CLXXIIL  What  the  difference  in  amount  of  bear 
ing  at  I  may  be  with  both  arms  fully  loaded,  can  not 
easily  be  determined  with  precision.  But  as  to  Fig. 
72,  it  is  deemed  entirely  safe  to  assume  that  at  least 
all  the  weight  at  j  and  k  will  bear  at  £,  in  all  cases  of 
load  sufficient  to  produce  a  maximum  strain  upon  any 
part  of  the  structure  on  the  right  from  the  point  a ; 
and  that  all  the  weight  from  b  to  i,  including  those 
points,  may  bear  at  a.  This  will  depend  somewhat 
upon  the  firmness  with  which  the  ends  are  brought  to 
bear  upon  abutments  when  in  position  for  use,  but 
without  load. 

Under  the  above  supposition  as  to  bearing  at  ls  the 
obliques  ml  and  mj  would  exert  horizontal  action  equal 
to  3W— ,  and  equal  to  that  of  ig,  and  half  that  of  gr  in 
the  opposite  direction ;  whence  gl  alone  of  the  lower 
chord  is  under  tension,  and  rm  of  the  upper  chord, 
under  compression  ;  but  in  neither  case  under  maxi 
mum  stress.  On  the  contrary,  ag  is  under  compres 
sion,  and  rx  under  tension,  being  in  each  case  a  maxi 
mum  stress  upon  a  considerable  portion  of  those  parts, 
as  will  be  determined  by  comparing  the  strains  of 
respective  parts  in  the  present  assumed  conditions, 
with  those  obtained  while  the  structure  swings  clear 
of  abutments. 

Representing,  as  usual  in  this  work,  the  long  diag 
onal  by  D,  and  the  short  and  steep  ones  by  D',  we  have 


SWING  DRAW  BRIDGES.  333 

^-  and  |p  factors  in  expressions  of  stresses  of  those 
classes  of  members  respectively,  and  for  convenience,  we 
will  substitute  m  for-?  and  n  for^-.  Then,  stress  of  iq 

and  gr,  in  case  of  full  load  upon  both  arms,  equals 
AVm,  for  each;  That  of  fs  and  et  equals  2Wm,  that 
ofrfw  an  ex  equals  3Wm,  and  that  of  bx  equals  4Wn. 

CLXXIV.  As  to  the  stress  of  chords,  half  the  hori 
zontal  action  of  gr,  being  taken  by  the  excess  of  thrust 

of  mr  over  hor.  action  of  iq,*  the  other  half,  f»W— J,  is 
opposed  by  tension  of  rs,  and  compression  of  gf.  This 
added  to  4Wp  for  hor.  action  of/sf  (making  ~  =  p), 

makes  5AVp  =•  tension  of  st,=  comp.  offe.  Add  4Wp 
for  action  of  et,  and  it  makes  9Wp  =  tension  of  tu,  — 
comp.  of  ed.  Adding  again  6~Wp  for  hor.  action  of  du, 
gives  15 Wp  »=  tension  of  ux,  =  comp.  of  dc.  Then, 
adding  6Wp  for  action  of  ex,  gives  21Wp  =  comp.  of 
be,  and  lastly,  adding  4Wp  for  action  of  bx,  we  have 
25TV~p  =  comp.  of  baza',  =  horizontal  action  of  xy  and 
xz.  This  all  falls  upon  xy  in  case  of  equal  arms. 

In  one  or  other  of  the  three  cases  above  considered 
(namely :  first,  arm  swung  clear  and  without  load  ; 
second,  arm  xl  fully  loaded;  third,  both  arms  fully 
loaded),  every  part  of  the  arm  xl  undergoes  its  great 
est  strain,  which  may  be  determined  by  comparing  the 
results  obtained  by  computing  the  strains  produced  in 

*  The  2W  upon  ml,  and  1W  upon  jm,  produce  thrust  equal  to 
o  W—  upon  mq,  which  equals  the  horizontal  action  of  iq,  -j-  half  that 

of  gr  in  the  opposite  direction,  leaving  W—  to  be  opposed  by  tension 
of  rs. 

\fs  sustaining  2W,  its  horizontal  action  =  4W— . 


334  BRIDGE  BUILDING. 

the  several  cases ;  §  except  that  ep  and  fo  may  snffer 
a  nominal  stress,  not  precisely  determinable,  under  a 
load  progressing  from  a  to  L  Also  gn  may  sustain 
some  more  weight  with  Lj  and  k  unloaded,  than  with 
the  truss  fully  loaded.  It  is  deemed  safe  to  provide 
that  gn  be  able  to  sustain  a  weight  of  |W;  /o,  to  sus 
tain  JW,  and  ep,  JW,  a  little  more  or  less  as  the  judg 
ment  or  calculations  of  the  designer  may  dictate. 

The  preceding  explanations  are  thought  to  be  suffi 
cient  to  guide  as  to  the  computation  of  stresses  upon 
the  other  arm  of  the  bridge,  whether  equal  or  unequal 
to  the  arm  al. 

The  superstructures  of  swing  bridges  should  be 
thoroughly  cross-tied  and  braced  laterally,  and  the 
king  posts  (represented  by  ax  and  yz),  well  secured  by 
arch  braces  or  other  efficient  means  transversely  :  and 
if  the  space  az  be  too  great  for  floor  joists  or  rail  string 
ers  without  intermediate  support,  an  intermediate  beam 
may  be  suspended  from  the  crossing  point  of  ay  and 
xz,  or  stringers  may  be  trussed. 

CLXXY.  Whatever  advantages  either  of  these  plans 
(Figs.  71  and  72),  may  have  over  the  other,  are  pro 
bably  not  very  great.  I  find  a  greater  amount  of  ac 
tion  (stress  into  length  of  parts),  upon  material  in 
chords  of  the  long  arm,  in  plan  Fig.  71,  including  the 
suspension  rod  eb,  than  in  that  of  Fig.  72,  by  some  5 

£  It  will  be  seen  that  tu  is  under  less  tension  strain  (as  2Sw'p  to 
Mw'p),  and  ts  under  greater  strain  (as  21  to  20),  when  the  truss  is  on 
the  swing,  than  when  fully  loaded  on  both  arms  (upon  the  above 
assumptions  of  w=s'd-wf,  and  2W  bearing  at  I),  and  that  tn  has  the 
max.  tension  with  bridge  on  the  swing,  while  tx  has  its  maximum 
with  bridge  fully  loaded,  inn  is  always  under  compression.  In  the 
lower  chord,  e  is  the  changing  point,  and  parts  at  the  left  have  their 
max.  comp.  with  bridge  fully  loaded,  and  those  on  the  right,  when, 
on  the  swing. 


DRAW  BRIDGES.  335 

per  cent.  And  while  the  action  upon  diagonals  and 
verticals  may  be  a  little  greater  in  case  of  the  latter, 
the  extra  material  in  the  tower  frame  of  the  former,  is 
thought  to  be  an  overbalance  for  any  such  excess,  even 
including  the  greater  thrust  and  tension  in  the  con 
tinuation  of  chords  over  the  turn-table,  which  takes 
place  in  plan  Fig.  72. 

In  regard  to  convenience  of  construction  and  appear 
ance  of  structure,  also,  as  well  as  economy  of  material, 
the  latter  plan  is  thought  to  possess  some  advantage. 
Still  opinions  and  tastes  may  vary  as  to  this,  as  well  as- 
in  regard  to  other  matters. 

Regarding  the  ratio  of  length  to  depth  of  truss,  the 
same  rules  should  govern  in  plan  71,  as  in  the  case  of 
stationary  bridges  of  like  span.  In  spanning  channel* 
of  50  or  60  feet  in  width,  on  plan  72,  the  head  room 
required  for  the  traffic  will  govern,  and  depth  from  15 
to  18  feet,  according  to  span,  and  the  purposes  of  the 
bridge,  whether  for  common  or  railroad  travel,  wilS 
probably  be  found  expedient.  In  general,  circum 
stances  will  probably  dictate  a  variation  of  ratio  (of 
depth  of  truss  to  length  of  span),  ranging  from  J  to  J. 

TURN  TABLE. 

CLXXVI.  The  same  plan  of  turn  table  is  applicable 
with  equal  advantage  to  either  of  the  two  above  de 
scribed  plans  of  swing  bridge  trussing. 

A  common,  perhaps  the  most  common,  form  of  turn 
table  for  draw  bridges,  is  composed  of  rollers  act, 
Fig.  73,  arranged  in  circular  form,  and  rolling  between 
two  metallic  circular  rails,  of  which  one,  66,  is  fastened 
to  the  supporting  pier  />,  and  the  other,  cc,  inverted, 
and  attached  to  the  under  side  of  the  bridge  super 
structure. 


336 


UP.IDGE  BUILDING. 


The  rollers  are  in  the  form  of  conic  frusta,  or  seg 
ments  of  cones  having  their  vertices  meeting  at  the 
axis  of  motion  of  the  bridge ;  and  are  retained  in  posi 
tion  by  arms  radiating  from  a  central  hub,  and  serving 
as  axles  for  the  rollers;  or  secured  by  a  circular  frame, 

FIG.  73. 


B 


ff,  formed  of  two  concentric  iron  rings  (shown  com 
plete  in  the  upper,  but  only  in  section  in  the  lower 
diagram  of  Fig.  73),  one  inside,  and  the  other  outside 


TURN-TABLES.  337 

of  the  circle  of  rollers.  The  rollers  may  either  turn 
upon  pins  through  their  centres,  and  through  said  rings, 
or  the  pin  or  shaft  may  be  fast  in  the  roller,  and  turn 
with  it  upon  journals  running  in  gudgeon  boxes 
attached  to  or  formed  in  the  circular  frame  /.  The 
pins  or  axles  may  be  quite  small  (say  V  to  1 J  in  dia 
meter),  as  they  support  but  a  nominal  weight,  and  are 
only  required  to  maintain  the  proper  positions  and 
directions  of  the  axes  of  the  rollers. 

The  roller  frame,  as  well  as  the  upper  circular  rail 
running  upon  the  rollers,  must  be  connected  with  a 
central  hub  for  each  (as  they  do  not  turn  together), 
turning  upon  a  journal  or  pivot  attached  to  the  ma 
sonry  of  the  supporting  pier.  The  rails,  or  surfaces 
between  which  the  rollers  work,  are  beveled  to  fit  the 
conical  faces  of  the  rollers,  and,  in  order  to  work  in 
the  most  perfect  manner,  they  should  be  of  cast  iron, 
and  turned  off  by  a  tool  carried  by  the  arm  of  a  heavy 
revolving  vertical  shaft. 

The  diameter  of  the  circle  should  not  probably  be 
less  than  J  to  \  the  span  of  the  water  channel,  nor  less 
than  £  to  ^  the  width  of  superstructure,  and  the  dia 
meter  of  the  rollers,  not  greater  than  TV  to  J  of  the 
radius  of  the  circle  upon  which  they  travel.  Greater 
diameter  would  give  so  much  obliquity  of  face  as  to 
produce  too  strong  a  centrifugal  tendency.  The  face 
of  the  rail  should  have  a  width  of  2J  to  3  inches 
generally,  and  for  some  30°  opposite  each  king  post 
(transversely  of  the  bridge)  when  the  draw  is  in  position, 
a  width  about  twice  as  great,  and  as  great  as  the  face 
of  the  rollers.  This  is  to  give  sufficient  bearing  surface 
while  loads  are  passing,  when  nearly  the  whole  weight 
will  be  concentrated  upon  two  or  three  rollers  near 
each  of  those  positions. 
13 


338  BRIDGE  BUILDING. 

The  lower  rail  should  have  a  depth  (if  of  cast  iron), 
of  4  to  5  inches,  according  to  size  of  bridge  ;  and  the 
upper  and  inverted  one,  of  one  to  two  feet  (the  deeper 
the  stiffer),  and  in  both  cases,  they  will  generally  be 
cast  in  segments,  and  those  of  the  upper  one,  bolted 
together  by  flanges,  so  as  to  form  a  rigid  hoop,  over 
which  one  or  more  strong  beams,  BB,  crossing  at  quad- 
ran  tal  points  ee,  etc.  (or  at  the  angular  points  of  any 
rectangle  inscribed  in  the  circle),  should  form  supports 
for  the  king  posts  (ag,  and  ch,  Fig.  71),  the  space  gh,  being 
adjusted  to  an  equality  with  the  side  of  the  inscribed 
square  or  rectangle  of  the  rail  circle.  And,  the  nearer 
the  transverse  distance  between  king  posts  comes  to 
the  length  of  the  other  sides  of  the  said  inscribed  square 
or  rectangle,  the  less  stiffness  of  beams,  BB,  is  required ; 
that  is,  (7(7,  F.  73  representing  truss  chords,  and  dd,  the 
positions  of  king  posts,  the  nearer  the  d  points  come 
to  the  e  points,  the  less  is  the  transverse  action  upon 
the  beams  BB.  Hence  it  is  desirable  that  the  circle  of 
rollers  should  pass  directly  under  the  points  dd,  etc. 

CLXXVHL  An  intermediate  beam  may  be  in 
serted  between  BB,  and  over  the  centre  pivot,  resting 
upon  the  circle  cc,  to  support  floor  joists  or  rail 
stringers  over  the  long  stretch  between  BB.  Or  very 
stiff  diagonal  girders  ee,  and  e'e',  firmly  attached  by 
the  ends  to  the  circle  cc,  meeting  a  common  nucleus  at 
II,  and  so  arranged  as  to  have  an  adjustable  bearing 
upon  the  centre  pivot  (5  or  6  inches  in  diameter,  as  to 
size  of  draw),  enabling  any  desired  amount  of  the 
weight  of  structure  which  such  girders  can  support,  to 
be  thrown  upon  said  pivot,  and  thereby  relieving  the 
rollers,  a,  of  a  like  amount  of  pressure.  These  girders 
should  have  the  greatest  practicable  depth,  so  as  to  sus- 


TURN-TABLES.  339 

tain  as  great  a  proportion  of  the  weight  of  superstruc 
ture  as  may  be.  But  the  skill  and  judgment  of  engineers 
in  charge  of  specific  cases  respectively,  will  dictate  as 
to  the  minutiae  of  these  devices,  and  more  precise  de 
tail  will  not  be  attempted  in  this  place. 

CLXXIX.  This  plan  of  turn  table,  as  well  as  the 
one  hereafter  to  be  described,  is  worked  by  a  vertical 
shaft  attached  to  the  superstructure,  and  turned  by  one 
or  more  sweep  levers,  with  a  pinion  at  the  lower  end, 
taking  into  toothed  segments  attached  to  the  circular 
track  6,  or  to  the  masonry  of  the  pier  p  ;  and,  in  case 
more  power  be  required,  a  gear  wheel  takes  place  of 
the  sweeps  above  mentioned,  and  these  are  transferred 
to  a  second  shaft  and  pinion  working  into  said  gear 
wheel. 

The  table  above  described,  with  slight  modifications, 
is  extensively  in  use,  and,  when  well  constructed,  un 
doubtedly  works  as  easily  and  satisfactorily  as  can  be 
expected.  Still,  it  is  liable  to  some  objections,  among 
which  may  be  named  the  great  weight  of  the  ring  cc, 
constituting  or  carrying  the  inverted  rail,  and  the  great 
number  of  rollers,  «,  so  few  of  which  can  act  with  much 
effect  at  the  same  time.  For,  it  is  obvious  that  about 
two  rollers  under  each  king  post,  support  essentially 
the  whole  weight.  It  is  therefore  proper  that  when 
the  bridge  is  in  place,  each  king  post  should  stand  cen 
trally  between  two  consecutive  rollers ;  and,  that  the 
rollers  be  at  equal  distances  apart.  Then  there  will 
be  at  least  8  rollers  under  equal  pressure  at  all  times 
when  loads  are  in  transit,  and  when  rollers  receive  their 
greatest  pressure.  But  without  discussing  this  plan 
further  at  present,  I  proceed  to  describe  another  swing 
bridge  turn-table  devised  many  years  ago  by  myself, 


340 


BRIDGE  BUILDING. 


and  used  in  a  considerable  number  of  cases  with  most 
satisfactory  results. 

FIG.  74. 


THE  WHIPPLE  TURN  TABLE. 

CXXX.  Is  arranged  with  a  two  wheeled  truck  a, 
Fig.  74,  directly  under  each  king  post,  and  the  four 
connected  in  pairs  diagonally  by  an  inverted  triangular 
truss  to  each  pair.  These  trusses  consist  of  a  hollow 


TURN-TABLES.  341 

cylindrical  (or  conic  segmental)  brace  6,  running  from 
each  truck  frame  obliquely  downward  to  an  abutting 
block  c,  which  is  common  to  the  two  trusses,  with 
chords  or  ties  </,  from  truck  to  truck  for  each  pair. 

The  truck  wheels  are  from  20  to  24  inches  in  dia 
meter,  with  5  to  6  inches  width  of  rim,  and  with  short 
axles  or  shafts,  3  to  4  inches  in  diameter,  according  to 
dimensions  of  bridge.  The  axles  run  in  journal  boxes 
fitted  to  the  truck-frame  so  as  to  bring  the  axles  in  the 
direction  of  radii  to  the  circular  track  t,  upon  which 
the  trucks  are  to  run. 

The  truck  frame  consists  of  two  cast  iron  side  plates 
(of  which  g  and  h  present  an  outside  and  an  inside  view), 
of  an  I  formed  cross  section,  and  contour  as  seen  at  g. 
These  plates  upon  the  insides,  have  projecting  portions 
as  shown  by  the  dark  surface  of  diagram  A,  meeting 
from  opposite  plates,  in  the  centre  of  the  frame  at  a 
common  surface  of  contact,  and  forming  continuous 
tubes  or  sockets  through  the  frame,  which  serve  as 
media  through  which  the  ties  d,  act  upon  the  cylindri 
cal  braces  6,  thus  forming  a  rigid  truss,  which  should 
be  so  proportioned  as  to  be  able  to  support  (upon  the 
two  trusses),  the  whole  weight  of  superstructure,  throw 
ing  it  upon  the  centre  block  c. 

The  chord  ties  d,  of  the  two  trusses,  crossing  one 
another  upon  the  same  level,  are  kept  from  mutual  in 
terference  by  cutting  out  the  middle  portion  of  one 
set,  and  replacing  the  removed  part  with  two  pieces  to 
each  tie  bar,  one  passing  above  and  the  other  below  the 
single  continuous  rods  of  the  other  set,  as  shown  at/. 

The  block  c  has  a  cylindrical  cavity  in  the  under  side, 
10  to  12  inches  in  diameter,  and  about  7  inches  deep, 
into  which  is  fitted  (loosely)  a  solid  cylinder  entering 
about  4  inches  into  the  cavity,  and  leaving  a  space  of 


342  BRIDGE  BUILDIXG. 

structure  to  be  raised  essentially  free  from  bearing  up- 
some  3  inches  in  thickness  above,  to  be  occupied  by 
the  nuts  of  a  number  of  set  screws  s,  intended  to  force 
clown  said  internal  cylinder  upon  the  bed  plate  i,  and 
thus  relieve  the  truck  wheels  from  nearly  all  the  weight 
of  superstructure. 

The  bed  plate-  z,  has  a  socket  or  step  f  of  an  inch 
deep,  or  thereabouts,  with  a  hardened  steel  plate  in  the 
bottom,  to  receive  the  lower  part  of  the  cylinder  bear 
ing  upon  the  plate  i,  where  the  diameter  of  cylinder 
and  socket  should  be  graduated  to  the  proportion  most 
favorable  for  reducing  the  amount  of  friction.  A  di 
ameter  of  6  to  8  inches  is  thought  to  be  suitable  for 
draws  of  60  to  100  feet  opening,  while  the  part  of  the 
pivot  block  within  the  block  c  should  have  a  diameter 
of  10  or  12  inches,  in  order  to  afford  sufficient  surface 
for  the  set  screws  s  to  act  upon. 

The  bed  plate  i.  should  have  a  rim  about  the  step  to  re 
tain  oil,  and  the  surfaces  above  and  below  the  steel  plate 
should  have  radial  grooves  to  allow  the  penetration  of 
oil;  and  these  (grooves)  should  be  so  situated  as  to  admit 
of  their  being  probed,  to  prevent  their  getting  clogged. 

The  pivot  block  should  have  guides  to  prevent  its 
turning  in  the  cavity  of  the  block  c  ;  otherwise  it  might 
stick  in  the  step,  and  the  set  screws  slide  upon  its  upper 
surface ;  which  has  been  the  case  in  some  instances. 

A  groove  should  be  formed  in  the  under  side  of  the 
block  c,  near  the  edge,  to  keep  the  water  from  the  pivot ; 
and  the  screws-  s,  should  be  kept  secluded  from  water 
by  a  tin,  or  galvanized  iron  cap  shutting  over  a  rim  or 
ring  cast  upon  the  block  c,  outside  of  the  screw  hole?. 
Sufficient  vertical  movement  (1J  or  2  inches),  should 
be  allowed  to  the  pivot  cylinder,  to  enable  the  elasticity 
of  the  braces  and  ties,  b  and  d,  to  be  taken  up,  and  the 


TURN-TABLES.  343 

on  the  wheels  e,  as  the  bridge  will  move  much  more 
easily  with  the  bearing  upon  the  centre  pivot,  than  up. 
on  the  truck  wheels. 

The  king  posts  should  be  placed  over  the  centres  of 
trucks,  or,  when  this  can  not  be  done,  they  should  bear 
upon  transverse  beams  which  bear  upon  centres  of 
trucks.  In  all  cases,  the  bearing  upon  trucks  should 
be  through  the  medium  of  bolster  plates  so  formed  up 
on  the  under  side  as  to  touch  the  truck  frame  only  up 
on  a  space  an  inch  wide  or  less,  square  across  the  centre, 
as  indicated  by  the  parallel  lines  across  the.  trucks  in 
the  large  diagram  of  the  Figure  74.  Were  the  pressure 
applied  in  a  line  diagonally  across  the  truck,  it  would 
act  unequally  upon  the  journals,  and  produce  a  tortion 
strain  upon  the  truck  frame,  which  the  latter  might 
not  be  able  to  bear. 

Particular  care  should  be  taken  to  provide  convenient 
means  for  keeping  the  working  parts  thoroughly  oiled. 

The  superstructure  being  properly  adjusted  and 
balanced  upon  this  turn-table,  and  the  set  screws  s, 
forced  down  until  all  the  truck  wheels  can  be  easily 
made  to  slide  upon  the  rail  by  the  use  of  a  light  crow 
bar,  the  structure  will  turn  upon  its  centre  pivot, 
steadied  by  contact  of  truck  wheels  upon  the  rail, 
with  the  least  practicable  resistance,  and,  during  the 
transit  of  moving  loads,  the  wheels,  beincr  in  contact 

O  O 

with  the  rail,  are  in  readiness  to  sustain  the  additional 
weight  without  increase  of  pressure  upon  the  pivot,  or 
increased  strain  upon  the  diagonal  trusses. 

The  modes  and  means  for  the  application  of  power 
in  working  this  table,  as  well  as  the  preceding  one,  have 
already  been  described,  [CLXXIX],  and  the  description 
need  not  be  repeated.  They  need  no  illustration  by  dia 
gram,  and  are  not  shown  in  the  drawings. 


344  BRIDGE  BUILDING. 

The  plan,  Fig.  74,  requires  the  middle  portion  of  the 
supporting  pier  to  be  depressed  1J  to  2  feet,  as  shown 
at  p,  where  a  vertical  section  of  the  upper  part  of  the 
pier  is  represented;  and,  under  the  bed  plate  z,  should 
be  a  large  and  firmly  bedded  stone  capable  of  sustain 
ing  the  whole  weight  of  superstructure. 

This  plan  appears  to  answer  all  the  requisites  of  a 
draw-bridge  turn-table  by  the  most  direct  and  economi 
cal  means. 


LIFT  DRAW  BRIDGES. 

CLXXXI.  Under  this  designation  may  be  included 
all  movable  bridges  which  are  withdrawn  from  position 
by  being  raised,  instead  of  moved  horizontally  out  of 
place. 

Lift  bridges,  though  not  much  in  use  at  the  present 
day,  have  been  constructed  to  be  raised  bodily,  being 
counterpoised  by  weights  acting  over  pulleys  or  sheaves ; 
a  plan  scarcely  feasible  upon  waters  navigated  by  mast 
vessels,  or  steamers  with  high  smoke  stacks ;  as  must 
be  obvious  on  a  moment's  reflection. 

The  more  common  device  for  lift  draws,  is,  to  raise 
the  platform  from  a  horizontal  to  a  vertical  position,  by 
lifting  one  end,  while  the  other  turns  upon  a  hinge 
joint ;  the  operation  being  like  the  raising  of  a  trap 
door. 

This  plan  is  feasible  over  narrow  channels,  where 
vessels  may  be  slowly  warped  through.  But  the  pro 
cess  requires  so  much  time  as  to  seriously  impede  the 
land  traffic.  A  bridge  may  be  so  balanced  as  to  turn 
upon  a  horizontal  axis  about  as  easily  as  a  swing  bridge 
turns  upon  a  vertical  one.  But  the  means  available 


LIFT  DRAW  BRIDGES.  345 

for  applying  the  counterpoise  are  far  less  convenient, 
being  usually  the  action  of  weights  over  sheaves,  and, 
the  resistance  constantly  diminishing  as  the  bridge 
rises,  it  requires  a  complicated  arrangement  to  graduate 
the  action  of  the  counterpoise  to  an  equality  with  the 
resistance  at  all  stages  of  the  movement.  Still,  the 
thing  may  be  practicable,  were  the  object  of  sufficient 
utility  to  warrant  the  undertaking.  For  instance,  the 
counterpoise  may  be  permanently  attached  to  the  draw 
in  such  position  as  to  bring  the  common  centre  of 
gravity  in  the  line  of  the  axis  of  motion  ;  when  the 
only  resistance  would  be  the  friction  of  the  journals  at 
the  hinge  joint.  Again,  a  counterpoise  acting  upon  a 
windlass  might  raise  the  draw  by  chains  winding  upon 
a  fusee,  with  radius  increasing  as  resistance  diminishes. 
Or,  weight  might  be  mounted  upon  wheels,  and  run 
down  upon  a  curved  incline,  so  adjusted  as  to  diminish 
its  action  to  an  equality  with  the  resistance  at  the  dif 
ferent  stages. 

But  none  of  these  devices  are  suitable  for  effecting 
more  than  very  small  openings,  and  are  not  likely  to 
be  often  adopted.  They  will  therefore  be  passed  by 
with  a  mere  allusion. 

Lift  bridges  have  also  been  constructed  to  open  in 
the  middle  and  lift  both  ways.  By  this  means  wider 
openings  may  be  effected. 

But,  as  the  middle  portion  of  the  bridge  and  passing 
loads  must  be  sustained  by  the  lifting  chains,  this  plan 
is  not  well  adapted  to  any  but  light  traffic.     Such  a 
structure  over  the  Albany  Basin  broke  down  many 
years  ago  with  fatal  results.     Perhaps,  however,  the 
catastrophe  resulted  rather  from  the  imperfect  condi 
tion  or  faulty  construction  of  the  bridge,  than  from  in 
herent  defects  of  the  general  plan. 
44 


346  BRIDGE  BUILDING. 

Still,  this  can  hardly  be  classed  as  among  the  availa 
ble  plans  of  draw-bridge  construction  in  the  present 
state  of  advancement  in  civil  engineering. 

Finally,  unless  some  advantage  can  be  derived  from 
the  use  of  the  Whipple  Patent  Lift  Drawbridge,  which 
is  now  about  to  be  described,  we  may  fairly  conclude 
that  Lift  Draw-bridges,  like  retractile  ones,  are  to  be 
regarded  as  practically  obsolete. 

CLXXXII.  In  the  case  of  artificial  navigation  by 
horse  power,  where  only  head  room  of  10  or  12  feet  is 
required,  and  where  convenience  requires  the  grade 
upon  which  the  land  traffic  is  carried  on  to  be  but  little 
above  the  water  surface,  it  is  only  necessary  to  effect 
a  vertical  movement  of  a  few  feet,  to  afford  the  re 
quisite  head  room.  And  to  meet  such  cases,  a  plan 
has  lately  been  devised  by  myself,  for  which  Letters 
Patent  of  the  U.  S.  have  been  granted. 

WHIPPLE'S  PATENT  LIFT  DRAW  BRIDGE. 

This  plan  is,  to  construct  over  the  navigable  channel, 
stationary  trusses  (with  the  necessary  struts,  stays  and 
braces,  at  the  ends  and  upper  chords,  to  secure  per- 
manance  and  steadiness  laterally),  upon  corner  posts  or 
towers  (a,  Fig.  75)  of  stone,  wood  or  iron,  high  enough 
to  allow  the  required  head  room  for  navigation  under 
the  truss  chords;  the  towers  having  sufficient  width 
of  base,  or  other  provision  to  ensure  stability.  To 
the  parts  thus  prepared,  instead  of  a  stationary  travel- 
way,  a  movable  way,  cradle,  or  track,  6,  (extending  to 
the  edge  of  the  towing  path  J),  is  adapted  by  means  of 
the  suspension  rods  r,  to  the  upper  ends  of  which, 


347 


t 


?     3 

5"     | 


348  BRIDGE  BUILDING. 

near  the  lower  chords,  are/connected  the  chains  or 
ropes  c,  passing  over  the  sheaves  or  pulleys  e,  and  con 
necting  with  counterpoise  weights  iv,  extending  over 
the  whole  length  of  cradle,  and  so  adjusted  as  to  just 
balance  the  weight  of  cradle. 

The  rods  r,  except  those  near  the  abutment,  pass 
vertically  through  the  connecting  blocks  of  the  truss 
chords,  and  screw  into  cap  pieces  which  are  imme 
diately  above,  and  rest  upon  said  blocks,  when  the 
cradle  is  down,  and  serve  to  prevent  the  cradle  from 
descending  below  its  proper  level,  and  to  sustain  the 
weight  of  transient  loads  without  additional  stress 
upon  the  chains  or  pulleys. 

The  cap-piece  is  furnished  with  a  loop,  or  a  socket, 
as  may  be  required,  for  the  connection  of  the  chain  or 
wire  rope  <?,  passing  up  inside  of  the  hollow  truss 
post  standing  upon  the  connecting  block;  the  post 
having  a  slot,  or  opening  near  the  upper  end  upon  the 
inner  side,  to  receive  a  segment  of  the  sheave  reaching 
the  centre  of  the  post. 

The  sheaves,  except  the  endmost  on  the  left  (in  the 
diagram),  are  about  3  feet  in  diameter,  and  made  fast 
upon  longitudinal  line  shafts  I,  one  on  each  side  of 
the  bridge,  hung  in  composition  journal  boxes,  one 
upon  each  side  of  each  sheave,  suspended  from  cross 
beams  h.  The  sheave  next  the  end  of  truss,  is  about 
6  inches  less  in  diameter  than  the  others,  and  thrown 
inward  to  avoid  interference  with  the  diagonal  rods  of 
the  truss. 

Upon  each  line  shaft  near  the  centre,  is  a  bevel  gear 
wheel  #,  about  3  feet  in  diameter,  into  which  works  a 
pinion  upon  either  end  of  the  transverse  shaft  /,  to 
which  (shaft)  the  power  is  applied  for  raising  and 


LIFT  DRAW  BRIDGES.  849 

lowering  the  cradle  6;  and,  it  will  be  seen  that  on 
such  application  of  power  sufficient  to  overcome  the 
friction  of  the  working  parts,  the  cradle  being  exactly 
balanced  by  the  weights  w,  the  two  line  shafts,  with 
the  sheaves  upon  them  respectively,  must  revolve  uni 
formly,  carrying  the  ropes  along  in  the  grooves  of  the 
sheaves,  and  raising  or  lowering  all  parts  of  the  cradle 
uniformly,  while  the  balance  weights  w,  move  in  the 
opposite  direction. 

It  is  therefore  only  necessary  to  reverse  the  motion 
of  the  shaft/,  to  move  the  cradle  up  and  down  alter 
nately  as  often  as  required. 

The  sheaves  not  connected  with  the  line  shafts,  move 
with  the  others,  the  cradle  being  stiff  enough  to  over 
come  the  small  resistance  at  those  points,  since  the 
endmost  sheaves  sustain  only  half  as  much  weight  as 
the  intermediates. 

Working  loose  upon  the  shaft/,  is  the  large  gear 
wheel  n,  attatched  to  the  winding  drum  m,  and  carry 
ing  a  reversible  spring  catch  (not  shown)  which  plays 
into  the  teeth  of  the  ratchet  wheel  o,  made  fast  on  the 
shaft/.  Then,  by  applying  power  to  the  wheel  7?, 
with  the  catch  in  the  proper  position,  a  line  is  made 
to  wind  upon  the  drum  m,  (in  either  direction,  as  re 
quired)  so  as  to  raise  a  power  weighty,  capable  by  its 
descent,  of  raising  or  lowering  the  cradle  through  the 
required  space  in  a  few  seconds  of  time.  The  line 
raising  the  weight  p,  is  carried  from  the  drum  m,  by 
means  of  sheaves  s,  to  any  convenient  position. 

One  movement  of  the  cradle  being  effected,  the 
catch  is  reversed,  the  weight  p  is  immediately  wound 
up  in  the  opposite  direction,  and  retained  by  a  catch 
or  bolt  until  the  draw  requires  another  movement. 
Then,  the  weight  is  disengaged,  and  the  movement 


350  BRIDGE  BUILDING. 

effected  in  the  least  admissible  time.  Ten  seconds, 
with  a  properly  adjusted  power  weight,  is  estimated  to 
be  sufficient  for  a  movement  of  the  cradle  through  a 
space  of  12  feet,  while  the  winding  up  of  the  weight 
may  require  two  or  three  minutes  labor  of  a  man.  The 
operator  is  thus  enabled  to  condense  the  labor  of 
several  minutes  into  only  a  few  seconds. 

It  is  proposed  to  give  the  power  weight  twice  the 
force  necessary  to  overcome  the  friction,  allowing  one- 
half  to  overcome  inertia,  and  act  as  an  accelerating 
force ;  the  weight  being  made  to  run  down  and  be 
arrested  when  half  the  movement  has  been  effected, 
leaving  the  acquired  momentum  to  be  destroyed  by 
the  friction  during  the  other  half  of  the  movement. 
Thus  the  motion  will  stop  at  the  right  time  without 
concussive  shock. 

The  wheel  n,  to  which  the  winding  power  is  applied,, 
may  be  a  bevel  gear  wheel  driven  by  a  pinion  upon  the 
vertical  shaft  of  a  tread-wheel  or  a  sweep-lever,  or  a 
spur  gear  wheel  impelled  by  a  pinion  upon  a  horizon 
tal  counter-shaft ;  and  this  also  furnished  with  a  large 
gear  wheel  to  be  driven  by  a  pinion  upon  a  third  shaft 
furnished  with  a  hand  crank;  thus  reducing  the 
power  to  be  applied  to  tne  crank  to  any  required  de 
gree.  Further  detail  is  not  deemod  necessary  on  this 
occasion.  The  plan  is  expected  soon  to  be  subjected 
to  a  practical  test  of  its  capabilities. 

The  advantages  promised  by  the  adoption  of  this 
device,  in  the  situations  admitting  of  its  use,  are,  first, 
it  is  more  cheaply  constructed  than  a  swing  bridge  of 
like  span.  Second,  it  requires  no  more  space  for  ita 
operation  than  a  stationary  bridge,  while  the  swing 
draw  requires  several  times  as  much.  Third,  its  move 
ment  is  effected  in  a  fraction  of  the  time  required  by 


LIFT  DRAW  BRIDGES.  351 

any  other  draw  bridge,  whence  It  occasions  less  inter 
ruption  to  the  traffic  over  and  beneath  it.  This  last 
advantage  results  from  the  fact  that  there  is  not  more 
than  one-third  as  much  weight  to  be  put  in  motion, 
and  that  is  required  to  move  over  little  if  any  more 
than  one  quarter  (say  f )  of  the  space  of  the  average 
movement  of  the  material  of  a  swing  draw  of  the  same 
spun.  Hence,  the  inertia  to  be  overcome  in  starting 
and  stopping  the 'latter,  is  much  greater  than  in  case 
of  the  former.  For,  the  resistance  of  inertia  being  as 
the  mass  into  the  square  of  the  velocity  to  be  commu 
nicated  in  a  given  time,  to  give  to  thrice  the  mass,  3J 
times  the  velocity,  as  required  to  shift  these  draws  re 
spectively  in  the  same  time,  would  give  a  resistance  of 
inertia  more  than  36  times  as  great  in  one  case  as  in 
the  other,  and  require  36  times  as  much  power  to 
generate  the  velocity  in  the  given  time.  But  an  ac 
celerating  force  equal  to  the  friction,  acting  through 
half  the  time  of  the  movement,  generates  a  momentum 
in  the  lift  draw,  sufficient  to  overcome  the  friction  for 
the  other  half;  and,  the  friction  of  the  swing  draw 
being  little  if  any  greater  for  the  whole  movement 
than  that  of  the  lift  draw,  it  would  only  destroy  J8  part 
of  the  momentum  generated  in  the  swing  draw  during 
the  first  half  of  the  movement,  by  a  force  capable  of 
producing  that  movement  in  the  same  time  required 
by  the  lift  draw.  The  other  ||  of  the  acquired 
momentum  must  be  destroyed  without  useful  effect, 
in  order  to  avoid  severe  concussion  at  the  stopping 
point,  while  in  the  other  case  the  whole  acquired  mo 
mentum  may  be  utilized  in  overcoming  necessary 
friction,  so  that  no  power  need  be  wasted.  Therefore, 
without  extending  this  discussion,  already,  perhaps, 
carried  too  far,  it  may  safely  be  pronounced  practically 


352      .  BRIDGE  BUILDING. 

impossible  to  effect  the  movement  of  the  swing  draw, 
in  the  time  in  which  that  of  the  lift  draw  may  be  ac 
complished. 

After  all,  practical  test  is  generally  the  only  satisfac 
tory  means  of  determining  the  value  and  utility  of  any 
mechanical  device. 


SCIENTIFIC  BOOKS 

PUBLISHED   BY 

D.  YAIST  NOSTEAND, 

23  MURRAY  STREET  &  27  WARREN  STREET, 
NEW    YORK. 


Weisbach's  Mechanics. 

New  and  Revised  Edition. 

8vo.     Cloth.     $10.00. 

A   MANUAL    OF   THE    MECHANICS   OF   ENGINEEKING, 

and  of  the  Construction  of  Machines.  By  JULIUS  WEISBACII,  Pn. 
D.  Translated  from  the  fourth  augmented  and  improved  Ger 
man  edition,  by  ECKLEY  B.  COXE,  A.M.,  Mining  Engineer.  Vol. 
I. — Theoretical  Mechanics.  1,100  pages,  and  902  wo*d-cut 
illustrations. 

ABSTRACT  OP  CONTENTS. — Introduction  to  the  Calculus— The  General 
Principles  of  Mechanics — Phoronomics,  or  the  Purely  Mathematical  Theory 
of  Motion — Mechanics,  or  the  General  Physical  Theory  of  Motion  Statics  of 
Rigid  Bodies — The  Application  of  Statics  to  Elasticity  and  Strength — Dynam 
ics  of  Rigid  Bodies  -  Statics  of  Fluids  -  Dynamics  of  Fluids — The  Theory 
of  Oscillation,  etc. 

"  The  present  edition  is  an  entirely  new  work,  greatly  extended  and  very 
much  improved.  It  forms  a  text-book  which  must  find  its  way  into  the  hands, 
not  only  of  every  student,  but  of  every  engineer  who  desires  to  refresh  his  mem 
ory  or  acquire  clear  ideas  on  doubtful  points.'' — Manufacturer  and  Builder. 

"  We  hope  the  day  is  not  far  distant  when  a  thorough  course  of  study  and 
education  as  such  shall  be  demanded  of  the  practising  engineer,  and  with  this 
view  we  are  glad  to  welcome  this  translation  to  our  tongue  and  shores  of  one 
of  the  most  able  of  the  educators  of  Europe." — The  Technologist. 


6  SCIENTIFIC  BOOKS  PUBLISHED     BY 

Stoney  on  Strains. 

New  arid  Revised  Edition,  with  numerous  illustrations. 

Royal  8vo,  664  pp.    Cloth.    $12.50. 

THE  THEOKY  OF  STRAINS  IN  GIRDERS  and  Similar  Strae- 
tures,  with  Observations  on  the  Application  of  Theory  to  Practice, 
and  Tables  of  Strength  and  other  Properties  of  Materials.  By 
BINDON  B.  STONEY,  B.  A. 


Roebling's  Bridges. 

Imperial  folio.     Cloth.     $25.00. 

LONG  AND  SHORT  SPAN  RAILWAY  BRIDGES.  By  JOHW 
A.  ROEBLING,  C.  E.  Illustrated  with  large  copperplate  engrav 
ings  of  plans  and  views. 

List  of  Plates 

1.  Parabolic  Truss  Railway  Bridge.  2,  3,  4,  5,  6.  Details  of  Parabolic 
Truss,  with  centre  span  500  feet  in  the  clear.  7.  Plan  and  View  of  a  Bridge 
over  the  Mississippi  River,  at  St.  Louis,  for  railway  and  common  travel.  8,  9, 
10,  11,  12.  Details  and  View  of  St.  Louis  Bridge.  13.  Railroad  Bridge  over 
the  Ohio. 


Diedrichs'  Theory  of  Strains. 

8vo.     Cloth.    $5.00. 

A  Compendium  for  the  Calculation  and  Construction  of  Bridges, 
Roofs,  and  Cranes,  with  the  Application  of  Trigonometrical 
Notes.  Containing  the  most  comprehensive  information  in  re 
gard  to  the  Resulting  Strains  for  a  permanent  Load,  as  also  for 
a  combined  (Permanent  and  Rolling)  Load.  In  two  sections 
adapted  to  the  requirements  of  the  present  time.  By  JOHN  Dim>- 
KICHS.  Illustrated  by  numerous  plates  and  diagrams. 

"  The  want  of  a  compact,  universal  and  popular  treatise  on  the  Construc 
tion  of  Roofs  and  Bridges — especially  one  treating  of  the  influence  of  a  varia 
ble  load — and  the  unsatisfactory  essays  of  different  authors  on  the  subject, 
induced  me  to  prepare  this  work."  « 


D.   VAN  NOSTRAND. 


Whilden's  Strength,  of  Materials, 

12ra<x     Cloth.     $2,00, 

ON  THE.  STRENGTH  OF  MATERIALS  used  in  Engineering 
Construction.     By  J.  K.  WHILDEN, 


C ampin  on  Iron  Roofs. 

Large  8vo.     Cloth.     $2,00. 

ON  THE  CONSTRUCTION  OF  IRON  ROOFS.  A  Theoretical 
and  Practical  Treatise.  By  FEAXCIS  CAMPIN.  With  wood-cuts 
and  plates  of  Roofs  lately  executed. 

"  The  mathematical  formulas  are  of  an  elementary  kind,  and  the  process 
admits  of  an  easy  extension  so  as  to  embrace  the  prominent  varieties  of  iron, 
truss  bridges.  The  treatise,  though  of  a  practical  scientific  character,  may  be 
easily  mastered  by  any  one  familiar  with  elementary  mechanics  and  plane 
trigonometry." 

Holley's  Railway  Practice. 

1  voL  folio.     Cloth.     $12.00. 

AMERICAN  AND   EUROPEAN  RAILWAY  PRACTICE,   in 

the  Economical  Generation  of  Steam,  including  the  materials 
and  construction  of  Coal-burning  Boilers,  Combustion,  the  Varia 
ble  Blast,  Vaporization,  Circulation,  Super-heating,  Supplying 
and  Heating  Feed- water,  &c.,  and  the  adaptation  of  Wood  and 
Coke-burning  Engines  to  Coal-burning  ;  and  in  Permanent  Way, 
including  Road-bed,  Sleepers,  Rails,  Joint  Fastenings,  Street 
Railways,  &c.,  &c.  By  ALEXANDER  L.  HOLLEY,  B.  P.  With  77 
lithographed  plates. 

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struction  and  use  of  locomotives,  with  a  few  chapters  on  the  building  of  Rail 
roads.  *  *  *  All  these  subjects  are  treated  by  the  author,  who  is  a 
first-class  railroad  engineer,  in  both  an  intelligent  and  intelligible  manner.  The 
facts  and  ideas  are  well  arranged,  and  presented  in  a  clear  and  simple  style, 
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ed  as  indispensable  by  all  who  are  interested  in  a  knowledge  of  the  construc 
tion  of  railroads  and  rolling  stock,  or  the  working  of  locomotives." — Scientific 
American. 


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Henrici's  Skeleton  Structures. 

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SKELETON  STEUCTUEES,  especially  in  their  Application  to 
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With  folding  plates  and  diagrams. 

By  presenting  these  general  examinations  on  Skeleton  Structures,  with 
particular  application  for  Suspended  Bridges,  to  Engineers,  I  venture  to  ex 
press  the  hope  that  they  will  receive  these  theoretical  results  with  some  confi 
dence,  even  although  an  opportunity  is  wanting  to  compare  them  with  practi 
cal  results.  0.  H. 


Useful  Information  for  Railway  Men. 

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Compiled  by  W.  Gr.  HAMILTON,  Engineer.     Fifth    edition,  revised 
and  enlarged.     570  pages. 

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and,  indeed,  for  almost  every  class  of  persons  in  the  world.  The  '  informa 
tion  '  comprises  some  valuable  formulae  and  rules  for  the  construction  of 
boilers  and  engines,  masonry,  properties  of  steel  and  iron,  and  the  strength 
of  materials  generally." — Railroad  Gazette,  Chicago. 


Brooklyn  Water  Works. 

1  vol.  folio.     Cloth.     $25.00.  • 

A  DESCEIPTIVE  ACCOUNT  OF  THE  CONSTEUCTION  OF 
THE  WOEKS,  and  also  Eeports  on  the  Brooklyn,  Hartford, 
Belleville,  and  Cambridge  Pumping  Engines.  Prepared  and 
printed  by  order  of  the  Board  of  Water  Commissioners.  With 
59  illustrations. 

CONTENTS. — Supply  Ponds — The  Conduit  -Ridgewood  Engine  House  and 
Pump  Well — Ridgewood  Engines — Force  Mains — Ridgewood  Reservoir — 
Pipe  Distribution — Mount  Prospect  Reservoir — Mount  Prospect  Engine 
House  and  Engine — Drainage  Grounds — Sewerage  "Works — Appendix. 


D.  VAN  XOSTRAND. 


Kirkwood  on  Filtration. 

4to.     Cloth.     $15.00. 

REPORT  ON  THE  FILTRATION  OF  EIVER  WATERS,  for 

the  Supply  of  Cities,  as  practised  in  Europe,  made  to  the  Board 
of  Water  Commissioners  of  the  City  of  St.  Louis.  By  JAMES  P. 
KIRKWOOD.  Illustrated  by  30  double-plate  engravings. 

CONTENTS. — Report  on  Filtration — London  Works,  General— Chelsea 
Water  Works  and  Filters — Lambeth  Water  Works  and  Filters — Southwark 
and  Vauxhull  Water  Works  and  Filters — Grand  Junction  Water  Works  and 
Filters— West  Middlesex  Water  Works  and  Filters— New  River  Water 
Works  and  Filters — East  London  Water  Works  and  Filters — Leicester  Water 
Works  and  Filters — York  Water  Works  and  Filters — Liverpool  Water  Works 
and  Filters— Edinburgh  Water  Works  and  Filters— Dublin  Water  Works 
and  Filters— Perth  Water  Works  and  Filtering-  Gallery — Berlin  Water 
Works  and  Filters — Hamburg  Water  Works  and  Reservoirs — Altona  Water 
Works  and  Filters — Tours  Water  Works  and  Filtering  Canal — Angers  Water 
Works  and  Filtering  Galleries — Nantes  Water  Works  and  Filters — Lyons 
Water  Works  and  Filtering  Galleries — Toulouse  Water  Works  and  Filtering 
Galleries— Marseilles  Water  Works  and  Filters — Genoa  Water  Works  and 
Filtering  Galleries — Leghorn  Water  Works  and  Cisterns— Wakefield  Water 
Works  and  Filters — Appendix. 


Tnnner  on  Roll-Turning. 

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A  TREATISE  ON  ROLL-TURNING  FOR  THE  MANUFAC 
TURE  OF  IRON.  By  PETER  TUNNER.  Translated  and  adapted. 
By  JOHN  B.  PEARSE,  of  the  Pennsylvania  Steel  Works.  With 
numerous  wood-cuts,  8vo.,  together  with  a  folio  atlas  of  10  litho 
graphed  plates  of  Rolls,  Measurements,  &c. 

"  We  commend  this  book  as  a  clear,  elaborate,  and  practical  treatise  upon 
the  department  of  iron  manufacturing  operations  to  which  it  is  devoted. 
The  writer  states  in  his  preface,  that  for  twenty-five  years  he  has  felt  the 
necessity  of  such  a  work,  and  has  evidently  brought  to  its  preparation  the 
fruits  of  experience,  a  painstaking  regard  for  accuracy  of  statement,  and  a 
desire  to  furnish  information  in  a  style  readily  understood.  The  book  should 
be  in  the  hands  of  every  one  interested,  either  in  the  general  practice  of 
mechanical  engineering,  or  the  special  branch  of  manufacturing  operations  to 
which  the  work  relates.'  — American  Artisan. 


10  SCIENTIFIC  BOOKS  PUBLISHED  BY 

G-lynn  on  the  Power  of  Water. 

12mo.     Cloth.     $1.00. 

A  TREATISE  ON  THE  POWER  OF  WATER,  as  applied  to 
drive  Flour  Mills,  and  to  give  motion  to  Turbines  and  other 
Hydrostatic  Engines.  By  JOSEPH  GLYNN,  F.R.  S.  Third  edition, 
revised  and  enlarged,  with  numerous  illustrations. 


Hewson  on  Embankments. 

Svo.     Cloth.     $2.00. 

PRINCIPLES   AND    PRACTICE  OF  EMBANKING   LANDS 

from  River  Floods,  as  applied  to  the  Levees  of  the  Mississippi. 
By  WILLIAM  HEWSON,  Civil  Engineer. 

"  This  is  a  valuable  treatise  on  the  principles  and  practice  of  embanking 
lands  from  river  floods,  as  applied  to  the  Levees  of  the  Mississippi,  by  a  highly 
intelligent  and  experienced  engineer.  The  author  says  it  is  a  first  attempt 
to  reduce  to  order  and  to  rule  the  design,  execution,  and  measurement  of  the 
Levees  of  the  Mississippi.  It  is  a  most  useful  and  needed  contribution  to 
scientific  literature. — Philadelphia  Evening  Journal. 


G-riiner  on  Steel. 

8vo.  Cloth.     $3.50. 

THE  MANUFACTURE  OF  STEEL.  By  M.  L.  GRFNEII,  trans 
lated  from  the  French.  By  Lenox  Smith,  A.  M.,  E.  M.,  with  an 
appendix  on  the  Bessemer  Process  in  the  United  States,  by  the 
translator.  Illustrated  by  lithographed  drawings  and  wood-cuts. 

"  The  purpose  of  the  work  is  to  present  a  careful,  elaborate,  and  at  the 
same  time  practical  examination  into  the  physical  properties  of  steel,  as  well 
as  a  description  of  the  new  processes  and  mechanical  appliances  for  its  manufac 
ture.  The  information  which  it  contains,  gathered  from  many  trustworthy 
sources,  will  be  found  of  much  value  to  the  American  steel  manufacturer, 
who  may  thus  acquaint  himself  with  the  results  of  careful  and  elaborate  ex 
periments  in  other  countries,  and  better  prepare  himself  for  successful  com 
petition  in  this  important  industry  with  foreign  makers.  The  fact  that  this 
volume  i.s  from  the  pen  of  one  of  the  ablest  metallurgists  of  the  present  day, 
cannot  fail,  we  think,  to  secure  for  it  a  favorable  consideration. — Iron  Age. 


D.    VAN  NOSTRAND.  11 


Bauerman  on  Iron. 

12mo.  Cloth.     $3.00. 

TEEATISE  ON  THE  METALLURGY  OF  IEON.  Contain 
ing  outlines  of  the  History  of  Iron  Manufacture,  methods  of 
Assay,  and  analysis  of  Iron  Ores,  processes  of  manufacture  of 
Iron  and  Steel,  etc.,  etc.  By  H.  BATTEEMA.N.  First  American 
edition.  Revised  and  enlarged,  with  an  appendix  on  the  Martin 
Process  for  making  Steel,  from  the  report  of  Abrani  S.  Hewitt. 
Illustrated  with  numerous  wood  engravings. 

"  This  is  an  important  addition  to  the  stock  of  technical  works  published  in 
this  country.  It  embodies  the  latest  facts,  discoveries,  and  processes  con 
nected  with  the  manufacture  of  iron  and  steel,  and  should  be  in  the  hands  of 
every  person  interested  in  the  subject,  as  well  as  in  all  technical  and  scientific 
libraries." — Scientific  A  merican. 


Link  and  Valve  Motions,  by  W.  S. 
Auchincloss. 

8vo.  Cloth.     $3.00. 

APPLICATION  OF  THE  SLIDE  VALVE  and  Link  Motion  to 
Stationary,  Portable,  Locomotive  and  Marine  Engines,  with  netv 
and  simple  methods  for  proportioning  the  parts.  By  WILLIAM 
S.  AUCHINCLOSS,  Civil  and  Mechanical  Engineer.  Designed  as 
a  hand-book  for  Mechanical  Engineers,  Master  Mechanics, 
Draughtsmen  and  Students  of  Steam  Engineering.  All  dimen 
sions  of  the  valve  are  found  with  the  greatest  ease  by  means  of 
a  Printed  Scale,  and  proportions  of  the  link  determined  without 
the  assistance  of  a  model.  Illustrated  by  37  wood-cuts  and  21 
lithographic  plates,  together  with  a  copperplate  engraving  of  the 
Travel  Soale. 

All  the  matters  we  have  mentioned  are  treated  with  a  clearness  and  absence 
of  unnecessary  verbiage  which  renders  the  work  a  peculiarly  valuable  one. 
The  Travel  Scale  only  requires. to  be  known  to  bo  appreciated.  Mr.  A.  writes 
so  ably  on  his  subject,  we  wish  he  had  written  more.  London  En 
gineering. 

We  have  never  opened  a  work  relating  to  steam  which  seemed  to  us  better 
calculated  to  give  an  intelligent  mind  a  clear  understanding  of  the  depart 
ment  it  discusses. — Scientific  American. 


12  SCIENTIFIC  BOOKS  PUBLISHED  BY 

Slide  Valve  by  Eccentrics,  by  Prof. 
C,  W.  MacCord. 

4to.     Illustrated.    Cloth,     $4.00. 

A  PRACTICAL  TREATISE    ON    TH£    SLIDE  VALVE    BY 

ECCENTRICS,  examining  by  methods,  the  action  of  the  Eccen 
tric  upon  the  Slide  Valve,  and  explaining  the  practical  proces 
ses  of  laying  out  the  movements,  adapting  the  valve  for  its 
various  duties  in  the  steam-engine.  For  the  use  of  Engineers, 
Draughtsmen,  Machinists,  and  Students  of  valve  motions  in 
general.  By  C.  "W.  MACCORD,  A.  M.,  Professor  of  Mechanical 
Drawing,  Stevens'  Institute  of  Technology,  Hoboken,  N  J. 


Stillman's  Steam-Engine  Indicator. 

12mo.  Cloth.     $1.00. 

THE  STEAM-ENGINE  INDICATOR,  and  the  Improved  Mano 
meter  Steam  arid  Vacuum  Gauges ;  their  utility  and  application 
By  PAUL  STILLMAN.  New  edition. 


Bacon's  Steam-Engine  Indicator. 

12mo.  Cloth.     $1.00.     Mor.     $1.50. 

A  TREATISE  ON  THE  RICHARDS  STEAM-ENGINE  IN 
DICATOR,  with  directions  for  its  use.  By  CHARLES  T.  PORTER. 
Revised,  with  notes  and  large  additions  as  developed  by  Amer 
ican  Practice,  with  an  Appendix  containing  useful  formula)  and 
rules  for  Engineers.  By  F.  W.  BACON,  M.  E.,  Member  of  the 
American  Society  of  Civil  Engineers.  Illustrated.  Second  Edition 

In  this  work.  Mr.  Porter's  book  has  been  taken  as  the  basis,  but  Mr.  Bacon 
has  adapted  it  to  American  Practice,  and  has  conferred  a  great  boon  on 
American  Engineers. — Artisan. 


Bartol  on  Marine  Boilers. 

8vo.  Cloth.     $1.50. 

TREATISE  ON  THE  MARINE  BOILERS  OF  THE  UNITED 
STATES.     By  H.  B.  BARTOL.     Illustrated. 


D.   VAN  NOSTRAND.  13 

Gillmore's  Limes  and  Cements. 

Fourth  Edition.    Revised  and  Enlargd. 

8vo.    Cloth.     $4.00. 

PRACTICAL  TREATISE  ON  LIMES,  HYDRAULIC  CE 
MENTS,  AND  MORTARS.  Papers  on  Practical  Engineering, 

,  U.  S.  Engineer  Department,  No.  9,  containing  Reports  of 
numerous  experiments  conducted  in  New  York  City,  during  the 
years  1858  to  1861,  inclusive.  By  Q.  A.  GILLMORE,  Brig-General 
U.  S.  Volunteers,  and  Major  U.  S.  Corps  of  Engineers.  With 
numerous  illustrations. 

"  This  work  contains  a  record  of  certain  experiments  and  researches  made, 
under  the  authority  of  the  Engineer  Bureau  of  the  "War  Department  from 
1858  to  1861,  upon  the  various  hydraulic  cements  of  the  United  States,  and 
the  materials  for  their  manufacture.  The  experiments  were  carefully  made, 
and  are  well  reported  and  compiled. ' — Journal  Franklin  Institute. 


Gillmore's  Ooignet  Beton. 

8vo.     Cloth.     $2.50. 

COIGNET   BETON  AND  OTHER  ARTIFICIAL  STONE.     By 
Q.  A.  GILLMORE.     9  Plates,  Views,  etc. 

This  work  describes  with  considerable  minuteness  of  detail  the  several  kinds 
of  artificial  stone  in  most  general  use  in  Europe  and  now  beginning  to  be 
introduced  in  the  United  States,  discusses  their  properties,  relative  merits, 
and  cost,  and  describes  the  materials  of  which  they  are  composed.  .... 
The  subject  is  one  of  special  and  growing  interest,  and  wo  commend  the  work, 
embodying  as  it  does  the  matured  opinions  of  an  experienced  engineer  and 
expert. 


Williamson's  Practical  Tables. 

:  4to.     Flexible  Cloth.     $2.50. 

PRACTICAL  TABLES  IN  METEOROLOGY  AND  HYPSO- 
METRY,  in  connection  with  the  use  of  the  Barometer.  By  Col. 
R.  S.  WILLIAMSOM,  U.  S.  A. 


14          SCIENTIFIC  BOOKS  PUBLISHED  BY 

Williamson  on  the  Barometer. 

4to.     Cloth.     $15.00. 

ON  THE  USE  OF  THE  BAROMETER  ON  SURVEYS  AND 
RECONNAISSANCES.  Part  I.  Meteorology  in  its  Connec 
tion  with  Hypsometry.  Part  II..  Barometric  Hypsometry.  By 
R.  S.  WILLIAMSON,  Bvt.  Lieut-Col.  U.  S.  A.,  Major  Corps  of 
Engineers.  With  Illustrative  Tables  and  Engravings.  Paper1 
No.  15,  Professional  Papers,  Corps  of  Engineers. 

"  SAN  FRANCISCO,  CAL.,  Feb.  27, 1867. 
"  Gen.  A.  A.  HUMPHREYS,  Chief  of  Engineers,  U.  S.  Army  : 

"  GENERAL, — I  nave  the  honor  to  submit  to  you,  in  the  following  pages,  the 
results  of  my  investigations  in  meteorology  and  hypsometry,  made  -with  the 
view  of  ascertaining  how  far  the  barometer  can  be  used  as  a  reliable  instru 
ment  for  determining  altitudes  on  extended  lines  of  survey  and  reconnais 
sances.  These  investigations  have  occupied  the  leisure  permitted  roe  from  my 
professional  duties  during  the  last  ten  years,  and  I  hope  the  results  will  be 
deemed  of  sufficient  value  to  have  a  place  assigned  them  among  the  printed 
professional  papers  of  the  United  States  Corps  of  Engineers. 
"  Very  respectfully,  your  obedient  servant, 

"R.  S.  WILLIAMSON, 
"  Bvt.  Lt.-Col.  U.  S.  A.,  Major  Corps  of  U.  S.  Engineers." 


Yon  Cotta's  Ore  Deposits. 

8vo.     Cloth.     $4.00. 

TREATISE  ON  OEE  DEPOSITS.  By  BERNHARD  Vox  GOTTA, 
Professor  of  Geology  in  the  Royal  School  of  Mines,  Freidberg, 
Saxony.  Translated  from  the  second  German  edition,  by 
FREDERICK  PRIME,  Jr.,  Mining  Engineer,  and  revised  by  the 
author,  with  numerous  illustrations. 

"  Prof.  Von  Cotta  of  the  Freiberg  School  of  Mines,  is  the  author  of  the 
best  modern  treatise  on  ore  deposits,  and  we  are  heartily  glad  that  this  ad 
mirable  \vork  has  been  translated  and  published  in  this  country.  The  trans 
lator,  Mr.  Frederick  Prime,  Jr.,  a  graduate  of  Freiberg,  has  had  in  his  work 
the  great  advantage  of  a  revision  by  the  author  himself,  who  declares  in  a 
prefatory  note  that  this  may  be  considered  as  a  new  edition  (the  third,  of  his 
own  book. 

"  It  is  a  timely  and  welcome  contribution  to  the  literature  of  mining  in 
this  country,  and  we  are  grateful  to  the  translator  for  his  enterprise  and  good 
judgment  in  undertaking  its  preparation ;  while  we  recognize  with  equal  cor 
diality  the  liberality  of  the  author  in  granting  both  permission  and  assist- 
aace." — Extract  from  Review  in  Engineering  and  Mining  Journal. 


7>.  VAN  NO  STRAND.  15 

Plattner's  Blow-Pipe  Analysis. 

Second  edition.    Revised.    8vo.     Cloth.     $7.50. 

PLATTNER'S  MANUAL  OF  QUALITATIVE  AND  QUAN 
TITATIVE  ANALYSIS  WITH  THE  BLOW-PIPE.  Prom 
the  last  German  edition  Revised  and  enlarged.  By  Prof.  TH. 
RICHTER,  of  the  Royal  Saxon  Mining  Academy.  Translated  by 
Prof.  II.  B.  CORNWALL,  Assistant  in  the  Columbia  School  of 
Mines,  New  York ;  assisted  by  JOHN  H.  CASWELL.  Illustrated 
with  eighty-seven  wood-cuts  and  one  Lithographic  Plate.  560 
pages. 

"  Plattner's  celebrated  work  has  long  been  recognized  as  the  only  complete 
book  on  Blow-Pipe  Analysis.  The  fourth  German  edition,  edited  by  Prof. 
Kichter,  fully  sustains  the  reputation  which  the  earlier  editions  acquired  dur 
ing  the  lifetime  of  the  author,  and  it  is  a  source  of  great  satisfaction  to  us  to 
know  that  Prof.  Kichter  has  co-operated  with  the  translator  in  issuing  the 
American  edition  of  the  work,  which  is  in  fact  a  fifth  edition  of  the  original 
work,  being  far  more  complete  than  the  last  German  edition." — SillimarSs 
Journal. 

There  is  nothing  so  complete  to  be  found  in  the  English  language.  Platt 
ner's  book  is  not  a  mere  pocket  edition  ;  it  is  ivitended  as  a  comprehensive  guide 
to  all  that  is  at  present  known  on  the  blow-pipe,  and  as  such  is  really  indis 
pensable  to  teachers  and  advanced  pupils. 

"  Mr.  Cornwall's  edition  is  something  more  than  a  translation,  as  it  contains 
many  corrections,  emendations  and  additions  not  to  be  found  in  the  original. 
It  is  a  decided  improvement  on  the  work  in  it*  German  dress." — Journal  of 
Applied  Chemistry. 


Egleston's  Mineralogy. 

8rq.     Illustrated  with  34  Lithographic  Plates.     Cloth.     $4.50. 

LECTUEES  ON  DESCRIPTIVE  MINERALOGY,  Delivered 
at  the  School  of  Mines,  Columbia  College.  13 r  PIIOFESSOJJ  T. 
EGLESTON. 

These  lectures  are  what  their  title  indicates,  the  lectures  on  Mineralogy 
delivered  at  the  School  of  Minca  of  Columbia  College.  They  have  beea 
printed  for  the  students,  in  order  that  more  time  might  be  given  to  the  vari 
ous  methods  of  examining  and  determining  minerals.  The  second  part  has 
only  been  printed.  The  first  part,  comprising  crystallography  and  physical 
mineralogy,  will  be  printed  at  some  future  time. 


16  SCIENTIFIC  BOOKS  PUBLISHED  BY 

Pynchon's  Chemical  Physics. 

New  Edition.    Revised  and  Enlarged. 

Crown  8vo.     Cloth. 


INTRODUCTION  TO  CHEMICAL  PHYSICS,  Designed  for  the 
Use  of  Academies,  Colleges,  and  High  Schools.  Illustrated  with 
numerous  engravings,  and  containing  copious  experiments  with 
directions  for  preparing  them.  By  THOMAS  RUGGLES  PYNCHON, 
M.  A.,  Professor  of  Chemistry  and  the  Natural  Sciences,  Trinity 
College,  Hartford. 

Hitherto,  no  work  suitable  for  general  use,  treating  of  all  these  subjects 
within  the  limits  of  a  single  volume,  could  be  found  ;  consequently  ths  atten 
tion  they  have  received  has  not  been  at  all  proportionate  to  their  importance. 
It  is  believed  that  a  book  containing  so  much  valuable  information  within  so 
small  a  compass,  cannot  fail  to  meet  with  a  ready  sale  among  ail  intelligent 
persons,  while  Professional  men,  Physicians,  Medical  Students,  Photograph 
ers,  Telegraphers,  Engineers,  and  Artisans  generally,  will  find  it  specially 
valuable,  if  not  nearly  indispensable,  as  a  book  of  reference. 

"  We  strongly  recommend  this  able  treatise  to  our  readers  as  the  first 
work  ever  published  on  the  subject  free  from  perplexing  technicalities.  In 
style  it  is  pure,  in  description  graphic,  and  its  typographical  appearance  is 
artistic.  It  is  altogether  a  most  excellent  work." — Eclectic  Medical  Journal. 

"  It  treats  fully  of  Photography,  Telegraphy,  Steam  Engines,  and  the 
various  applications  of  Electricity.  In  short,  it  is  a  carefully  prepared 
volume,  abreast  with  the  latest  scientific  discoveries  and  inventions.'' — Hart 
ford  Courant. 

Plympton's  Blow-Pipe  Analysis. 

12mo.     Cloth.     $2.00. 

THE  BLOW-PIPE  :  A  System  of  Instruction  in  its  practical  use 
being  a  graduated  course  of  Analysis  for  the  use  of  students, 
and  all  those  engaged  in  the  Examination  of  Metallic  Combina 
tions.  Second  edition,  with  an  appendix  and  a  copious  index. 
By  GEORGE  "W-  PLYMPTON,  of  the  Polytechnic  Institute,  Brooklyn. 

"  This  mamial  probably  has  no  superior  in  the  English  language  as  a  text 
book  for  beginners,  or  as  a  guide  to  the  student  working  without  a  teacher. 
To  the  latter  many  illustrations  of  the  utensils  and  apparatus  required  in 
using  the  blow-pipe,  as  well  as  the  fully  illustrated  description  of  the  blow 
pipe  flame,  will  be  especially  serviceable."— New  York  Teaclwr. 


.    VAN  JFOSTRAJSTD. 


lire's  Dictionary. 

Sixth   Edition. 

London,  1872. 
3  vols.     8vo.     Cloth,  $25.00.     Half  Russia,  $32.50. 

DICTTONAEY  OF  AETS,  MANUFACTURES,  AND  MINES. 
By  ANDREW  URE,  M.D.  Sixth  edition.  Edited  by  BOBERT  HUNT, 
F.E.S.,  greatly  enlarged  and  rewritten. 


Brande  and  Cox's  Dictionary. 

Neiv  Edition. 

London,  1872. 
3  rols.    8vo.    Cloth,  $20.00.    Half  Morocco,  $27.50. 

A  Dictionary  of  Science,  Literature,  and  Art.     Edited  by  \V.  T. 
BRANDE  and  Eev.  GEO.  W.  Cox.     New  and  enlarged  edition. 


Watt's  Dictionary  of  Chemistry. 

Supplementary  Volume. 

8vo.    Cloth.     $9.00. . 

This  volume  brings  the  Record  of  Chemical  Discovery  down  to  the  end  of 
the  year  1869,  including  also  several  additions  to,  and  corrections  of,  former 
results  which  have  appeared  in  1870  and  1871. 

*#*  Complete  Sets  of  the  Work,  New  and  Revised  edition,  including-  above 
supplement  C  vols.  8vo.  Cloth.  $62.00. 


Rammelsberg's  Chemical  Analysis. 

8vo.     Cloth.     $2.25. 

GUIDE  TO  A  COUESE  OF  QUANTITATIVE  CHEMICAL 
ANALYSIS,  ESPECIALLY  OF  MINERALS  AND  FUR 
NACE  PEODUCTS.  Illustrated  by  Examples.  By  C.  F. 
Translated  by  J.  TOWLER,  M.D. 


This  work  has  been  translated,  and  is  now  published  expressly  for  those 
students  in  chemistry  whose  time  and  other  studies  in  colleges  do  not  permit 
them  to  enter  "upon  the  more  elaborate  and  expensive  treatises  of  Fresenius 
and  others.  It  is  the  condensed  labor  of  a  master  in  chemistry  and  of  a  prac 
tical  analyst. 


18          SCIENTIFIC  BOOKS  PUBLISHED  BY 

Eliot  and  Storer's  Qualitative 
Chemical  Analysis. 

New  Edition,  Revised. 

12mo.     Illustrated.     Cloth.     $1.50. 

A  COMPENDIOUS  MANUAL  OF  QUALITATIVE  CHEMI 
CAL  ANALYSIS.  By  CHARLES  W.  ELIOT  and  FRA^K  H.  STORER. 
Revised  with  the  Cooperation  of  the  Authors,  by  WILLIAM  RIP- 
LEY  NICHOLS,  Professor  of  Chemistry  in  the  Massachusetts  Insti 
tute  of  Technology. 

"  This  Manual  has  great  merits  as  a  practical  introduction  to  the  science 
and  the  art  of  which  it  treats.  It  contains  enough  of  the  theory  and  practice 
of  qualitative  analysis,  "  in  the  wet  way,"  to  bring-  out  all  the  reasoning  in 
volved  in  the  science,  and  to  present  clearly  to  the  student  the  most  approved 
methods  of  the  art.  It  is  specially  adapted  for  exercises  and  experiments  in 
the  laboratory;  and  yet  its  classifications  and  manner  of  treatment  are  so 
systematic  and  logical  throughout,  as  to  adapt  it  in  a  high  degree  to  that 
higher  class  of  students  generally  who  desire  an  accurate  knowledge  of  the 
practical  methods  of  arriving  at  scientific  facts." — Lutfieran  Observer. 

"  We  wish  every  academical  class  in  the  land  could  have  the  benefit  of  the 
fifty  exercises  of  two  hours  each  necessary  to  master  this  book.  Chemistry 
would  cease  to  be  a  mere  matter  of  memory,  and  become  a  pleasant  experi 
mental  and  intellectual  recreation.  We  heartily  commend  this  little  volume 
to  the  notice  of  those  teachers  who  believe  in  using  the  sciences  as  means  of 
mental  discipline." — College  Courant. 


Craig's  Decimal  System. 

Square    32mo.     Limp.     50c. 

WEIGHTS  AND  MEASURES.  An  Account  of  the  Decimal 
System,  with  Tables  of  Conversion  for  Commercial  and  Scientific 
Uses.  By  B.  F.  CRAIG,  M.  D. 

"  The  most  lucid,  accurate,  and  useful  of  all  the  hand-books  on  this  subject 
that  we  have  yet  seen.  It  gives  forty-seven  tables  of  comparison  between  the 
English  and  French  denominations  of  length,  area,  capacity,  weight,  and  the 
Centigrade  and  Fahrenheit  thermometers,  with  clear  instructions  how  to  use 
them ;  and  to  this  practical  portion,  which  helps  to  make  the  transition  as 
easy  as  possible,  is  prefixed  a  scientific  explanation  of  the  errors  in  the  metric 
system,  and  how  they  may  be  corrected  in  the  laboratory." — Nation. 


D.   VAN  NOSTRAND.  19 

Nugent  on  Optics. 

12mo.      Cloth,     $2:00 

TREATISE  ON  OPTICS  ;  or,  Light  and  Sight,  theoretically  and 
practically  treated ;  with  the  application  to  Fine  Art  and  Indus 
trial  Pursuits.  By  E.  NUGENT.  With  one  hundred  and  three 
illustrations. 

"  This  book  is  of  a  practical  rather  than  a  theoretical  kind,  and  is  de 
signed  to  afford  accurate  and  complete  information  to  all  interested  in  appli 
cations  of  the  science." — Hound  Table. 


Barnard's  Metric  System. 

8vo.     Brown  cloth.     $3.00. 

THE   METRIC  SYSTEM  OF  WEIGHTS   AND  MEASURES. 

An  Address  delivered  before  the  .Convocation  of  the  University  of 
the  State  of  New  York,  at  Albany,  August,  1871.  By  FREDERICK 
A.  P.  BARNARD,  President  of  Columbia  College,  New  York  City. 
Second  edition  from  the  Revised  edition  printed  for  the  Trustees 
of  Columbia  College.  Tinted  paper. 

'*  It  is  the  best  summary  of  the  arguments  in  favor  of  the  metric  weights 
and  measures  with  which  we  are  acquainted,  not  only  because  it  contains  in 
small  space  the  leading  facts  of  the  case,  but  because  it  puts  the  advocacy  of 
that  system  on  the  only  tenable  grounds,  namely,  the  great  convenience  of  a 
decimal  notation  of  weight  and  measure  as  well  as  money,  the  value  of  inter 
national  uniformity  in  the  matter,  and  the  fact  that  this  metric  system  is 
adopted  and  hi  general  use  by  the  majority  of  civilized  nations." —  Tlie  Nation* 


The  Young  Mechanic. 

Illustrated.     12mo.      Cloth.     $1.75. 

THE  YOUNG  MECHANIC.  Containing  directions  for  the  use 
of  all  kinds  of  tools,  and  for  the  construction  of  steam  engines 
and  mechanical  models,  including  the  Art  of  Turning  in  Wood 
and  Metal.  By  the  author  of  "The  Lathe  and  its  Uses,"  etc 
From  the  English  edition,  with  corrections. 


20  SCIENTIFIC  BOOKS  PUBLISHED  BY 

Harrison's  Mechanic's  Tool-Book. 

12mo.    Cloth.    $1.50, 

MECHANIC'S  TOOL  BOOK,  with  practical  rules  and  suggestions, 
for  the  use  of  Machinists,  Iron  Workers,  and  others.  By  \V.  B. 
HARRISON,  Associate  Editor  of  the  "  American  Artisan."  Illustra 
ted  with  44  engravings. 

"  This  work  is  specially  adapted  to  meet  the  wants  of  Machinists  and  work 
ers  in  iron  generally.  It  is  made  up  of  the  \rork-day  experience  of  an  intelli 
gent  and  ingenious  mechanic,  who  had  the  faculty  of  adapting  tools  to  various 
purposes.  The  practicability  of  his  plans  and  suggestions  are  made  apparent 
even  to  the  unpractised  eye  by  a  series  of  well-executed  wood  engravings." — 
Philadelphia  Inquirer. 

Pope's  Modern  Practice  of  the  Elec 
tric  Telegraph. 

Eighth  Edition.    8vo.    Cloth     $2.00. 

A  Hand-book  for  Electricians  and  Operators.  By  FBANK  L.  POPS. 
Seventh  edition.  Revised  and  enlarged,  and  fully  illustrated. 

Extract  from  Letter  of  Prof.  Morse. 

"  I  have  had  time  only  cursorily  to  examine  its  contents,  but  this  examina 
tion  has  resulted  in  great  gratification,  especially  at  the  fairness  and  unpre 
judiced  tone  of  your  whole  work. 

"  Your  illustrated  diagrams  are  admirable  and  beautifully  executed. 

"  I  think  all  your  instructions  in  the  use  of  the  telegraph  apparatus  judi 
cious  and  correct,  and  I  most  cordially  wish  you  success." 

Extract  from  Letter  of  Prof.  O.  W.  Hough,  of  the  Dudley  Observatory. 

"  There  is  no  other  work  of  this  kind  in  the  English  language  that  con 
tains  in  so  small  a  compass  so  much  practical  information  in  the  application 
of  galvanic  electricity  to  telegraphy.  It  should  be  in  the  hands  of  every  one 
interested  in  telegraphy,  or  the  use  of  Batteries  for  other  purposes." 


Morse's  Telegraphic  Apparatus. 

Illustrated.     8vo.     Cloth.     $2.00. 

EXAMINATION  OF  THE  TELEGRAPHIC  APPARATUS 
AND  THE  PROCESSES  IN  TELEGAPHY.  By  SAMUEL  F. 
B.  MOBSE,  LL.D.,  United  States  Commissioner  Paris  Universal 
Exposition,  1867. 


D,  VAN  tfOSTXAND.  21 

Sabine's  History  of  the  Telegraph. 

12mo.  Cloth.     $1.25. 

HISTORY  AND   PROGRESS   OF    THE    ELECTRIC    TELE- 
f  GRAPH,    with   Descriptions   of  some    of   the    Apparatus.     By 
ROBEBT  SAJBINE,  C.  E.     Second  edition,  with  additions. 

CONTENTS.— I.  Early  Observations  of  Electrical  Phenomena.  II.  Tele 
graphs  by  Fractional  Electricity.  III.  Telegraphs  by  Voltaic  Electricity. 
IV.  Telegraphs  by  Electro-Magnetism  and  Magneto-Electricity.  V.  Tele 
graphs  now  in  use.  VI.  Overhead  Lines.  VII.  Submarine  Telegraph  Lines. 
VIII.  Underground  Telegraphs.  IX.  Atmospheric  Electricity. 


Haskins*    Galvanometer, 

Pocket  form.     Illustrated.    Morocco  tucks.    $2.00. 

THE  GALVANOMETER,  AND  ITS  USES;   a  Manual  for 
Electricians  and  Students.    By  0.  H.  HASKINS. 

"  We  hope  this  excellent  little  work  will  meet  with  the  sale  its  merits 
entitle  it  to.  To  every  telegrapher  who  owns,  or  uses  a  Galvanometer,  or 
ever  expects  to,  it  will  be  quite  indispensable." — The  Telegrapher. 


Culley's  Hand-Book  of  Telegraphy. 

8vo.    Cloth.    $6.00. 

A  HAND-BOOK  OF  PRACTICAL  TELEGRAPHY.  By 
R.  S.  CULLEY,  Engineer  to  the  Electric  and  International 
Telegraph  Company.  Fifth  edition,  revised  and  enlarged. 

-Fuivdl  8fioJJ rr'Q  a'iljLxbf i j ;  i ' 

Foster's  Submarine  Blasting. 

4to.     Cloth.     $3.50. 

SUBMARINE  BLASTING  in  Boston  Harbor,  Massachusetts- 
Removal  of  Tower  and  Corwin  Rocks.  By  JOHN  G.  FOSTEB, 
Lieutenant-Colonel  of  Engineers,  and  Brevet  Major- General,  U. 
S.  Army.  Illustrated  with  seven  plates. 

LIST  OF  PLATES. — 1.  Sketch  of  the  Narrows,  Boston  Harbor.  2. 
Townsend  s  Submarine  Drilling  Machine,  and  Working  Vessel  attending. 
3.  Submarine  Drilling  Machine  employed.  4.  Details  of  Drilling  Machine 
employed.  5.  Cartridges  and  Tamping  used.  6.  Fuses  and  Insulated  Wires 
used.  7.  Portable  Friction  Battery  used. 


22  SCIENTIFIC  BOOKS  PUBLISHED  BY 

"X, 

Barnes'  Submarine  Warfare. 

8™.     Cloth.     $5.00. 

SUBMARINE  WARFARE,  DEFENSIVE  AND  OFFENSIVE. 

Comprising  a  full  and  complete  History  of  the  Invention  of  the 
Torpedo,  its  employment  in  War  and  results  of  its  use.  De 
scriptions  of  the  yarious  forms  of  Torpedoes,  Submarine  Batteries 
and  Torpeclo  Boats  actually  used  in  War.  Methods  of  Ignition 
by  Machinery,  Contact  Fuzes,  and  Electricity,  and  a  full  account 
of  experiments  made  to  determine  the  Explosive  Force  of  Gun 
powder  under  Water.  Also  a  discussion  of  the  Offensive  Torpedo 
system,  its  effect  upon  Iron-Clad  Ship  systems,  and  influence  upon 
Future  Naval  Wars.  By  Lieut. -Commander  Joux  S.  BAEXES, 
IT.  S.  N.  With  twenty  lithographic  plates  and  many  wood-cuts. 

"  A  book  important  to  military  men,  and  especially  so  to  engineers  and  ar 
tillerists.  It  consists  of  an  examination  of  the  various  offensive  and  defensive 
engines  that  have  been  contrived  for  submarine  hostilities,  including  a  discus 
sion  of  the  torpedo  system,  its  effects  upon  iron-clad  ship-systems,  and  its 
probable  influence  upon  future  naval  wars.  Plates  of  a  valuable  character 
accompany  the  treatise,  which  affords  a  useful  history  of  the  momentous  sub 
ject  it  discusses.  A  great  deal  of  useful  information  is  collected  in  its  pages, 
especially  concerning  the  inventions  of  SCIIOI.L  a»d  VEIIDU,  and  of  JONES' 
and  HUNT'S  batteries,  as  well  as  of  other  similar  machines,  and  the  use  in 
submarine  operations  of  gun-cotton  and  nitro-glycerine." — N*  T.  Times* 


Randall's  Quartz  Operator's  Hand- 
Book. 

12mo.     Cloth.     $2.00. 

QUARTZ  OPERATOR'S    HAND-BOOK.     By   P.  M.  RANDALL. 

New  edition,  revised  and  enlarged.     Fully  illustrated.  • 

The  object  of  this  work  has  been  to  present  a  clear  and  comprehensive  ex 
position  of  mineral  veins,  ami  the  means  and  modes  chiefly  employed  for  the 
mining  and  working  of  their  ores — more  especially  those  containing  gold  and 
silver. 


D.    VAN  NOSTRAND.  23 


Mitchell's  Manual  of  Assaying. 

8vo.     Cloth.     $10.00, 

A  MANUAL  OF  PEACTICAL  ASSAYING.    By  JOHN  MITCHELL. 
Third  edition.     Edited  by  WILLIAM  CKOOKES,  F.E.S. 

In  this  edition  are  incorporated  all  the  late  important  discoveries  in  Assay 
ing  made  in  this  country  and  abroad,  and  special  care  is  devoted  to  the  very 
important  Volumetric  and  Colorimetric  Assays,  as  well  as  to  the  Blow-Pipe 


Benet's  Chronoscope. 

Second  Edition. 

Illustrated.     4to.     Cloth.     $3.00. 

ELECTEO-BALLISTIC  MACHINES,  and  the  Schultz  Chrono- 
scope.  By  Lieutenant-Colonel  S.  V.  BEN ET,  Captain  of  Ordnance, 
U.  S.  Army. 

CONTENTS.—1.  Ballistic  Pendulum.  2.  Gun  Pendulum.  3.  Use  of  Elec 
tricity.  4.  Navez' Machine.  5.  Vignotti's  Machine,  with  Plates.  6.  Benton's 
Electro-Ballistic  Pendulum,  with  Plates.  7.  Leur's  Tro-Pendulum  Machine 
8.  Schultz's  Chronoscope,  with  two  Plates. 


Michaelis'  Chronograph. 

4to.     Illustrated.     Cloth.     $3.00. 

THE  LE  BOULENGE  CHEONOGEAPH.  With  three  litho 
graphed  folding  plates  of  illustrations.  By  Brevet  Captain  0  E. 
MICHAELIS,  First  Lieutenant  Ordnance  Corps,  U.  S.  Army. 

"  The  excellent  monograph  of  Captain  Michaelis  enters  minutely  into  the 
details  of  construction  and  management,  and  gives  tables  of  the  times  of  flight 
calculated  upon  a  given  fall  of  the  chronometer  for  all  distances.  < 
Michaelis  has  done  good  service  in  presenting  this  work  to  his  brother  officers, 
describing,  as  it  does,  an  instrument  which  bids  fair  to  be  in  constant  use  in 
our  future  ballistic  experiments.'—^^  and  Navy  Journal. 


24          SCIENTIFIC  BOOKS  PUBLISHED  BY 

Silversmith's  Hand-Book. 

Fourth  Edition. 

Illustrated.     12mo.     Cloth.     $3,00. 

A  PRACTICAL  HAND-BOOK  FOE  MINERS,  Metallurgists, 
and  Assayers,  comprising  the  most  recent  improvements  in  the 
disintegration,  amalgamation,  smelting,  and  parting  of  the 
Precious  Ores,  with  a  Comprehensive  Digest  of  the  Mining 
Laws.  Greatly  augmented,  revised,  and  corrected.  By  JULIUS 
SILVERSMITH.  Fourth  edition.  Profusely  illustrated.  1  vol. 
12mo.  Cloth.  $3.00. 

One  of  the  most  important  features  of  this  work  is  that  in  which  the 
metallurgy  of  the  precious  metals  is  treated  of.  In  it  the  author  has  endeav 
ored  to  embody  all  the  processes  for  the  reduction  and  manipulation  of  the 
precious  ores  heretofore  successfully  employed  in  Grermany,  England,  Mexico, 
and  the  United  States,  together  with  such  as  have  been  more  recently  invented, 
and  not  yet  fully  tested — all  of  which  are  profusely  illustrated  and  easy  of 
comprehension. 


Simms'  Levelling. 

8vo.     Cloth.     $2.50. 

A  TREATISE  ON  THE  PRINCIPLES  AND  PRACTICE  OF 
LEVELLING,  showing  its  application  to  purposes  of  Railway 
Engineering  and  the  Construction  of  Roads,  &c.  By  FREDERICK 
W.  SIMMS,  C.  E.  From  the  fifth  London  edition,  revised  and 
corrected,  with  the  addition  of  Mr.  Law's  Practical  Examples  for 
Setting  Out  Railway  Curves.  Illustrated  with  three  lithographic 
plates  and  numerous  wood-cuts. 

"  One  of  the  most  important  text-books  for  the  general  surveyor,  and  there 
is  scarcely  a  question  connected  with  levelling  for  which  a  solution  would  be 
sought,  but  that  would  be  satisfactorily  answered  by  consulting  this  volume." 
— Mining  Jvumal. 

"  The  text-book  on  levelling  in  most  of  our  engineering  schools  and  col 
leges." — -Engineers. 

"  The  publishers  have  rendered  a  substantial  service  to  the  profession, 
especially  to  the  younger  members,  by  bringing  out  the  present  edition  of 
MJ.  Simms  useful  work." — Engineering. 


D.  VAN  NO  STRAND.  25 

Stuart's    Successful    Engineer. 

18mo.    Boards.    50  cents. 

HOW  TO  BECOME  A  SUCCESSFUL  ENGINEER:  Being 
Hints  to  Youths  intending  to  adopt  the  Profession.  By 
BERNARD  STUART,  Engineer.  Sixth  Edition. 

"A  valuable  little  book  of  sound,  sensible  advice  to  young  men  who 
wish  to  rise  in  the  most  important  of  the  professions." — Scientific  American. 


Stuart's  Naval  Dry  Docks. 

Twenty-four  engravings  on  steel. 
Fourth  Edition. 

4to.     Cloth.     $6.00. 

THE  NAVAL  DRY  DOCKS   OF    THE    UNITED    STATES. 
By  CHARLES  B.  STUAET.  Engineer  in  Chief  of  the  United  IS  tales 

Navy. 

List  of  Illustrations. 

Pumping  Engine  and  Pumps — Plan  of  Dry  Dock  and  Pump- Well -Sec 
tions  of  Dry  Dock — Engine  House — Iron  Flpating  Gate — Details  of  Floating 
Gate — Iron  Turning  Gate — Plan  of  Turning  Gate— Culvert  Gate— Filling 
Culvert  Gates— Engine  Bed — Plate,  Pumps,  and  Culvert — Engine  House 
Roof — Floating  Sectional  Dock — Details  of  Section,  and  Plan  of  Turn-Tables 
— Plan  of  Basin  and  Marine  Railways — Plan  of  Sliding  Frame,  and  Elevation 
of  Pumps — Hydraulic  Cylinder — Plan  of  Gearing  for  Pumps  and  End  Floats 
— Perspective  View  of  Dock,  Basin,  and  Railway — Plan  of  Basin  of  Ports 
mouth  Dry  Dock — Floating  Balance  Dock — Elevation  of  Trusses  and  the  Ma 
chinery  —  Perspective  View  of  Balance  Dry  Dock 


Free  Hand  Drawing. 

Profusely  Illustrated.     18mo.    Boards.    50  centa. 

A  GUIDE  TO  ORNAMENTAL,  Figure,   and  Landscape  Draw 
ing.     By  an  Art  Student. 

CONTENTS.— Materials  employed  in  Drawing,  and  how  to  use  them — On 
Lines  and  how  to  Draw  them-^On  Shading — Concerning  lines  and  shading, 
with  applications  of  them  to  simple  elementary  subjects — Sketches  from  Na 
ture. 


26  SCIENTIFIC  BOOKS  PUBLISHED  BY 

\  \ 

Minifie's  Mechanical  Drawing. 

Eighth  Edition. 

Royal  8vo.     Cloth.     $4.00. 

A  TEXT-BOOK  OF  GEOMETRICAL  DBAWING-  for  the  use 
of  Mechanics  and  Schools,  in  which  the  Definitions  and  Bales  of 
Geometry  are  familiarly  explained  ;  the  Practical  Problems  are 
arranged,  from  the  most  simple  to  the  more  complex,  and  in  their 
description  technicalities  are  avoided  as  much  as  possible.  With 
illustrations  for  Drawing  Plans,  Sections,  and  Elevations  of 
Buildings  and  Machinery ;  an  Introduction  to  Isornetrical  Draw 
ing,  and  an  Essay  on  Linear  Perspective  and  Shadows.  Illus 
trated  with  over  2(K)  diagrams  engraved  on  steel.  By  WM. 
MINIFIE,  Architect.  Eighth  Edition.  With  an  Appendix  on  the 
Theory  and  Application  of  Colors. 

"  It  is  the  best  work  on  Drawing1  that  we  have  ever  seen,  and  is  especially  a 
text-book  of  Geometrical  Drawing1  for  the  use  of  Mechanics  and  Schools.  No 
young  Mechanic,  such  as  a  Machinist,  Engineer,  Cabinet-Maker,  Millwright, 
or  Carpenter,  should  be  without  it." — Scientific  American. 

"  One  of  the  most  comprehensive  works  of  the  kind  ever  published,  and  can 
not  but  possess  great  value  to  builders.  The  style  is  at  once  elegant  and  sub 
stantial. ' — Pennsylvania  Inquirer. 

"  Whatever  is  said  is  rendered  perfectly  intelligible  by  remarkably  well- 
executed  diagrams  on  steel,  leaving  nothing  for  mere  vague  supposition  ;  and 
the  addition  of  an  introduction  to  isometrical  drawing,  linear  perspective,  and 
the  projection  of  shadows,  winding  up  with  a  useful  index  to  technical  terms." 
—  Glasgow  Mechanics'  Journal. 

B3?F°  The  British  Government  has  authorized  the  use  of  this  book  in  their 
schools  of  art  at  Somerset  House,  London,  and  throughout  the  kingdom. 


Minifie's  Geometrical  Drawing. 

New  Edition.    Enlarged. 

12mo.     Cloth.     $2.00. 

GEOMETEICAL  DEAWING.  Abridged  from  the  octavo  edition, 
for  the  use  of  Schools.  Illustrated  with  48  steel  plates.  New 
edition,  enlarged. 

'"  It  i  well  adapted  as  a  text-book  of  drawing  to  be  used  in  our  High  Schools 
and  Academies  where  this  useful  branch  of  the  fine  arts  has  been  hitherto  too 
much  neglected." — Boston  Journal. 


D.    VAN  NOSTRANJ).  27 

Bell  on  Iron  Smelting. 

8vo.     Cloth.     $6.0J. 

CHEMICAL  PHENOMENA  OF  IRON  SMELTING.  An  ex 
perimental  and  practical  examination  of  the  circumstances  which 
determine  the  capacity  of  the  Blast  Furnace,  the  Temperature 
of  the  Air,  and  the  Proper  Condition  of  the  Materials  to  be 
operated  upon.  By  I.  LOWTHIAN  BELL. 

"  The  reactions  -which  take  place  in  every  foot  of  the  blast-furnace  have 
been  investigated,  and  the  nature  of  every  step  in  the  process,  from  the  intro 
duction  of  the  raw  material  into  the  furnace  to  the  production  of  the  pig  iron, 
has  been  carefully  ascertained,  and  recorded  so  fully  that  any  one  in  the  trade 
can  readily  avail  themselves  of  the  knowledge  acquired  ;  and  we  have  no  hes 
itation  in  saying  that  the  judicious  application  of  such  knowledge  will  do 
much  to  facilitate  the  introduction  of  arrangements  which  will  still  further 
economize  fuel,  and  at  the  same  time  permit  of  the  quality  of  the  resulting 
metal  being  maintained,  if  not  improved.  The  volume  is  one  which  no  prac 
tical  pig  iron  manufacturer  can  afford  to  be  without  if  he  be  desirous  of  en 
tering  upon  that  competition  which  nowadays  is  essential  to  progress,  and 
in  issuing  such  a  work  Mr.  Bell  has  entitled  himself  to  the  best  thanks  of 
every  member  of  the  trade." — London  Mining  Journal. 


Zing's  Notes  on  Steam. 

Thirteenth  Edition. 

8vo.     Cloth.     $2.00. 

LESSONS  AND  PEACTICAL  NOTES  ON  STEAM,  the  Steam- 
Engine,  Propellers,  &c.,  &c.,  for  Young  Engineers,  Students,  and 
others.  By  the  late  W.  R.  KING,  U.  S.  N.  Revised  by  Chief- 
Engineer  J.  W.  KIXG,  U.  S.  Navy. 

"  This  is  one  of  the  best,  because  eminently  plain  and  practical  treatises  on 
the  Steam  Engine  ever  published. ' — Philadelphia  Press. 

This  is  the  thirteenth  edition  of  a  valuable  work  of  the  late  W.  H.  King, 
U.  S.  N.  It  contains  lessons  and  practical  notes  on  Steam  and  the  Steam  En 
gine,  Propellers,  etc.  It  is  calculated  to  be  of  great  use  to  young  marine  en 
gineers,  students,  and  others.  The  text  is  illustrated  and  explained  by  nu 
merous  diagrams  and  representations  of  machinery .  —  Boston  Daily  Adver 
tiser. 

Text-book  at  the  U.  S.  Naval  Academy,  Annapolis. 


28          SCIENTIFIC  BOOKS  PUBLISHED  BY 

Burgh's  Modern  Marine  Engineering. 

One  thick  4to  vol.     Cloth.     $25.00.     Half  morocco.     $30.00. 

MODEEN  MARINE  ENGINEERING,  applied  to  Paddlo  and 
Screw  Propulsion.  Consisting  of  36  Colored  Plates,  259  Practical 
Wood-cut  Illustrations,  and  403  pages  of  Descriptive  Matter,  the 
whole  being  an  exposition  of  the  present  practice  of  the  follow 
ing  firms  :  Messrs.  J.  Penn  &  Sons ;  Messrs.  Maudslay,  Sons  & 
Field  ;  Messrs.  James  Watt  &  Co. ;  Messrs.  J.  &  Gr.  Ronnie  ; 
Messrs.  R.  Napier  &  Sons  ;  Messrs.  J.  &  W.  Dudgeon  ;  Messrs. 
Ravenhill  &  Hodgson ;  Messrs.  Humphreys  &  Tenant ;  Mr. 
J.  T.  Spencer,  and  Messrs.  Forrester  &  Co.  By  N.  P.  BURGH, 
Engineer. 

PRINCIPAL  CONTENTS. — General  Arrangements  of  Engines,  11  examples 
— General  Arrangement  of  Boilers,  14  examples  —  General  Arrangement  of 
Superheaters,  11  examples — Details  of  'Oscillating  Paddlo  Engines,  04  ex 
amples — Condensers  for  Screw  Engines,  both  Injection  and  Surface,  20  ex 
amples — Details  of  Screw  Engines,  20  examples — Cylinders  and  Details  of 
Screw  Engines,  21  examples— Slide  Valves  and  Detail?,  7  examples— Slide 
Valve,  Link  Motion,  7  examples — Expansion  Valves  and  Gear,  10  exam 
ples — Details  in  General,  30  exam  pies --Screw  Propeller  and  Fittings,  13  ex 
amples  Engine  and  Boiler  Fittings,  28  examples  In  relation  to  the  Princi 
ples  of  the  Marine  Engine  and  Boiler,  33  examples. 

Notices  of  the  Press. 

"  Every  conceivable  detail  of  the  Marine  Engine,  under  all  its  various 
forms,  is  profusely,  and  we  must  add,  admirably  illustrated  by  a  multitude 
of  engravings,  selected  from  the  best  and  most  modern  practice  of  the  first 
Marine  Engineers  of  the  day.  The  chapter  on  Condensers  is  peculiarly  valu 
able.  In  one  word,  there  is  no  other  work  in  exist*,  nee  which  will  bear  a 
moment's  comparison  with  it  as  an  exponent  of  the  skill,  talent  and  practical 
experience  to  which  is  duo  the  splendid  reputation  enjoyed  by  many  British 
Marine  Engineers."  -  Engineer. 

"  This  very  comprehensive  work,  which  was  issued  in  Monthly  parts,  has 
just  been  completed.  It  contains  large  and  full  drawings  and  copious  de 
scriptions  of  most  of  the  best  examples  of  Modern  Marine  .Engines,  and  it  is 
a  complete  theoretical  and  practical  treatise  on  the  subject  of  Marine  Engi 
neering."  American  Artisan. 

This  is  the  only  edition  of  th»  above  work  with  the  beautifully  colored 
plates,  and  it  is  out  of  print  in  England. 


J).   VAN  NOSTRAND.  29 

Bourne's  Treatise  on  the  Steam  En 
gine. 

Ninth  Edition. 

Illustrated.     4to.     Cloth.     $15.00. 

TREATISE  ON  THE  STEAM  ENGINE  in  its  various  applica 
tions  to  Mines,  Mills,  Steam  Navigation,  Railways,  and  Agricul 
ture,  with  the  theoretical  investigations  respecting  the  Motive 
Power  of  Heat  and  the  proper  Proportions  of  Steam  Engines. 
Elaborate  Tables  of  the  right  dimensions  of  every -part,  and 
Practical  Instructions  for  the  Manufacture  and  Management  of 
every  species  of  Engine  in  actual  use.  By  JOHN  BOUKNE,  being 
the  ninth  edition  of  "  A  Treatise  on  the  Steam  Engine,"  by 
the  "  Artisan  Club."  Illustrated  by  thirty-eight  plates  and  five 
hundred  and  forty-six  wood-cuts. 

As  Mr.  Bourne's  work  has  the  great  merit  of  avoiding  unsound  and  imma 
ture  views,  it  may  safely  be  consulted  by  all  who  are  really  desirous  of  ac 
quiring  trustworthy  information  on  the  subject  of  which  it  treats.  During 
the  twenty-two  years  which  have  elapsed  from  the  issue  of  the  first  edition, 
the  improvements  introduced  in  the  construction  of  the  steam  engine  have 
been  both  numerous  and  important,  and  of  these  Mr.  Bourne  has  taken  care 
to  point  out  the  more  prominent,  and  to  furnish  the  reader  with  such  infor 
mation  as  shall  enable  him  readily  to  judge  of  their  relative  value.  This  edi 
tion  has  been  thoroughly  modernized,  and  made  to  accord  with  the  opinions 
and  practice  of  the  more  successful  engineers  of  the  present  day.  All  that 
the  book  professes  to  give  is  given  with  ability  and  evident  care.  The  scien 
tific  principles  which  are  permanent  are  admirably  explained,  and  reference 
is  made  to  many  of  the  more  valuable  of  the  recently  introduced  engines.  To 
express  an  opinion  of  the  value  and  utility  of  such  a  work  as  The  Artisan 
Club's  Treatise  on  the  Steam  Engine,  which  has  passed  through  eight  editions 
already,  woxild  bo  superfluous ;  but  it  may  be  safely  staged  that  the  work  is 
worthy  the  attentive  study  of  aM.  either  engaged  in  the  manufacture  of  Bteam 
engines  or  interested  in  economizing  the  use  of  steam. —  Mining  Journal. 


Islierwood's  Engineering  Precedents. 

Two  Vols.  in  One.     8vo.     Cloth.     $2.50. 

ENGINEERING  PRECEDENTS  FOR  STEAM  MACHINERY. 
Arranged  in  the  most  practical  and  useful  manner  for  Engineers. 
By  B.  F.  ISHEKWOOD,  Civil  Engineer,  U.  S.  Navy.  With  illus 
trations. 


30          SCIENTIFIC  BOOKS  PUBLISHED  BY 


Ward's  Steam  for  the  Million. 

New  and  Revised  Edition. 

8vo.  Cloth.     $1.00. 

STEAM  FOE  THE  MILLION.  A  Popular  Treatise  on  Steam 
and  its  Application  to  the  Useful  Arts,  especially  to  Naviga 
tion.  By  J.  H.  WAED,  Commander  U.  S.  Navy.  New  and  re 
vised  edition. 

A  most  excellent  work  for  the  young  engineer  and  general  reader.  Many 
facts  relating  to  the  management  of  the  boiler  and  engine  -are  set  forth  with  a 
simplicity  of  language  and  perfection  of.  detail  that  bring  the  subject  home 
to  the  reader. — American  Engineer. 


Walker's  Screw  Propulsion. 

8vo.     Cloth.     75  cents. 

NOTES  ON  SCREW  PROPULSION,  its  Rise  and  History.     By 
Capt.  W.  H.  WALKER,  U.  S.  Navy. 

Commander  Walker's  book  contains  an  immense  amount  of  concise  practi 
cal  data,  and  every  item  of  information  recorded  fully  proves  that  the  various 
points  bearing  upon  it  have  been  well  considered  previously  to  expressing  an 
opinion. — Tendon  Mining  Journal. 


Page's  Earth's  Crust. 

18mo.     Cloth.     75  cents. 

THE  EARTH'S  CRUST :    a   Handy   Outline   of  Geology.      By 
DAVID  PAGE. 

"  Such  a  work  as  this  was  much  wanted — a  work  giving  in  clear  and  intel 
ligible  outline  the  leading  facts  of  the  science,  without  amplification  or  irk 
some  details.  It  is  admirable  in  arrangement,  and  clear  and  easy,  and,  at  the 
same  time,  forcible  in  style.  It  will  lead,  wo  hope,  to  the  introduction  of 
Geology  into  many  schools  that  have  neither  time  nor  room  for  the  study  of 
large  treatises." — TJie  Museum. 


D.  VA  N  NOS  TRA  ND.  3 1 

Rogers'  G-eology  of  Pennsylvania. 

3  Vols.  4to,  with  Portfolio  of  Maps.     Cloth.     $30.00. 

THE  GEOLOGY  OF  PENNSYLVANIA.  A  Government  Sur 
rey.  With  a  general  view  of  the  Geology  of  the  United  States, 
Essays  on  the  Coal  Formation  and  its  Fossils,  and  a  description 
of  the  Coal  Fields  of  North  America  and  Great  Britain.  By 
HENRY  DAHWIN  ROGERS,  Late  State  Geologist  of  Pennsylvania. 
Splendidly  illustrated  with  Plates  and  Engravings  in  the  Text. 

It  certainly  should  be  in  every  public  library  ^nroughout  the  country,  and 
likewise  in  the  possession  of  all  students  of  Geology.  After  the  final  sale  of 
these  copies,  the  work  will,  of  course,  become  more  valuable. 

The  work  for  the  last  five  years  has  been  entirely  out  of  the  market,  but  a 
few  copies  that  remained  in  the  hands  of  Prof.  Rogers,  in  Scotland,  at  the 
time  of  his  death,  are  now  offered  to  the  public,  at  a  price  which  is  even 
below  what  it  was  originally  sold  for  when  first  published. 


Morfit  on  Pure  Fertilizers. 

"With  28  Illustrative  Plates.     8vo.     Cloth.     $20.00. 

A  PRACTICAL  TREATISE  ON   PURE   FERTILIZERS,  and 

the  Chemical  Conversion  of  Rock  Guanos,  Marlstones,  Coprolites, 
and  the  Crude  Phosphates  of  Lime  and  Alumina  Generally,  into 
yarious  Valuable  Products.  By  CAMPBELL  MORFIT,  M.D.,  F.C.S. 


Sweet's  Report  on  Coal. 

8vo.     Cloth.     $3.00. 

SPECIAL  REPORT  ON  COAL  ;  showing  its  Distribution,  Classi 
fication,  and  Cost  delivered  over  different  routes  to  various  points 
in  the  State  of  New  York,  and  the  principal  cities  on  the  Atlantic 
Coast.  By  S.  H.  SWEET.  With  maps. 


Colburn's  Gas  Works  of  London. 

I2ino.      Boards.     60  cents. 
GAS  WORKS  OF  LONDON.     By  ZEBAH  COLBUWT. 


32  SCIENTIFIC  BOOKS  PUBLISHED  BY 

The  Useful  Metals  and  their  Alloys ; 
Scoffren,  Truran,  and  others. 

Fifth  Edition. 

8vo.     Half  calf.     $3.75. 

THE  USEFUL  METALS  AND  THEIR  ALLOYS,  including 
MINING  VENTILATION,  MINING  JURISPRUDENCE 
AND  METALLURGIC  CHEMISTRY  employed  in  the  conver 
sion  of  IRON,  COPPER,  TIN,  ZINC,  ANTIMONY,  AND 
LEAD  ORES,  with  their  applications  to  THE  INDUSTRIAL 
ARTS.  By  JOHN  SCOFFKEN,  WILLIAM  TRTJRAN,  WILLIAM  CLAY, 
ROBERT  OXLAND,  WILLIAM  FAIRBAIBN,  W.  C.  AITKIN,  and  WIL 
LIAM  VOSE  PICKETT. 


Collins1  Useful  Alloys. 

18mo.     Flexible.     75  cents. 

THE  PRIVATE  BOOK  OF  USEFUL  ALLOYS  and  Memo 
randa  for  Goldsmiths,  Jewellers,  etc.  By  JAMES  E.  COLLINS 

This  little  book  is  compiled  from  notes  made  by  the  Author  from  the 
papers  of  one  of  the  largest  and  most  eminent  Manufacturing  Goldsmiths  and 
Jewellers  in  this  country,  and  as  the  firm  is  now  no  longer  in  existence,  and  the 
Author  is  at  present  engaged  in  some  other  undertaking,  he  now  offers  to  the 
public  the  benefit  of  his  experience,  and  in  so  doing  he  begs  to  state  that  all 
the  alloys,  etc.,  given  in  these  pages  may  be  confidently  relied  on  as  being 
thoroughly  practicable. 

The  Memoranda  and  Receipts  throughout  this  book  are  also  compiled 
from  practice,  and  will  no  doubt  be  found  useful  to  the  practical  jeweller. 
—Shirley,  July,  1871. 

Joynsorfs  Metals  Used  in  Construction. 

12mo.    Cloth.     75  cents. 

THE  METALS  USED  IN  CONSTRUCTION :  Iron,  Steel, 
Bessemer  Metal,  etc.,  etc.  By  FRANCIS  HERBERT  JOYNSON.  Il 
lustrated. 

"  In  the  interests  of  practical  science,  we  are  bound  to  notice  this  work  ; 
and  to  those  who  wish  further  information,  we  should  say,  buy  it ;  and  the 
outlay,  we  honestly  believe,  will  be  considered  well  spent."  —  Scientific 
Review. 


D.   VAN  NOSTRAND.  33 


Holley's  Ordnance  and  Armor. 

493  Engravings,     Half  Roan,  $10.00.     Half  Russia,  $12.00. 

A  TEEATISE  ON  ORDNANCE  AND  ARMOR— Embracing 
Descriptions,  Discussions,  and  Professional  Opinions  concerning 
the  MATERIAL,  FABRICATION,  Requirements,  Capabilities,  and  En 
durance  of  European  and  American  Guns,  for  Naval,  Sea  Coast, 
and  Iron-clad  Warfare,  and  their  RIFLING,  PROJECTILES,  and 
BREECH-LOADING;  also,  Results  of  Experiments  against  Armor, 
from  Official  Records,  with  an  Appendix  referring  to  Gun-Cotton, 
Hooped  Guns,  etc.,  etc.  By  ALEXANDER  L.  HOLLEY,  B.  P.  948 
pages,  493  Engravings,  and  147  Tables  of  Results,  etc. 

CONTENTS. 

CHAPTER  I. — Standard  Guns  and  their  Fabrication  Described:  Section  1. 
Hooped  Guns ;  Section  2.  Solid  Wrought  Iron  Guns ;  Section  3.  Solid  Steel 
Guns;  Section  4.  Cast-Iron  Guns.  CHAPTER  II. — The  Requirements  of  Guns, 
Armor:  Section  1.  The  Work  to  be  done;  Section  2.  Heavy  Shot  at  Low  Ve 
locities;  Sections.  Small  Shot  at  High  Velocities;  Section  4.  The  two  Sys 
tems  Combined ;  Section  5.  Breaching  Masonry.  CHAPTER  III. — The  Strains 
and  Structure  of  Guns:  Section  1.  Resistance  to  Elastic  Pressure;  Section  2. 
The  Effects  of  Vibration;  Section  3.  The  Effects  of  Heat.  CHAPTER  IV.— 
Cannon  Metals  and  Processes  of  Fabrication:  Section  1.  Elasticity  and  Ductil. 
ity;  Section  2.  Cast-Iron;  Section  3.  Wrought  Iron;  Section  4.  Steel;  Sec 
tion  5.  Bronze ;  Section  6.  Other  Alloys.  CHAPTER  V. — Rifling  and  Projec 
tiles  ;  Standard  Forms  and  Practice  Described ;  Early  Experiments ;  The 
Centring  System  ;  The  Compressing  System ;  The  Expansion  System ;  Armor 
Punching  Projectiles ;  Shells  for  Molten  Metal ;  Competitive  Trial  of  Rifled 
Guns,  1862;  Duty  of  Rifled  Guns:  General  Uses,  Accuracy,  Range,  Velocity, 
Strain,  Liability  of  Projectile  to  Injury ;  Firing  Spherical  Shot  from  Rifled 
Guns ;  Material  for  Armor-Punching  Projectiles ;  Shape  of  Armor-Punching 
Projectiles;  Capacity  and  Destructiveness  of  Shells;  Elongated  Shot  from 
Smooth  Bores;  Conclusions;  Velocity  of  Projectiles  (Tabled  CHAPTER  VI.— 
Breech-Loading  Advantages  and  Defects  of  the  System ;  Rapid  Firing  and 
Cooling  Guns  by  Machinery ;  Standard  Breech-Loaders  Described.  Part  Sec 
ond  :  Experiments  against  Armor ;  Account  of  Experiments  from  Official 
Records  in  Chronological  Order.  APPENDIX. — Report  on  the  Application  of 
Gun-Cotton  to  Warlike  Purposes — British  Association,  1863;  Manufacture  and 
Experiments  in  England ;  Guns  Hooped  with  Initial  Tension — History;  How 
Guns  Burst,  by  Wiard,  Lyman's  Accelerating  Gun ;  Endurance  of  Parrott 
and  Whitworth  Guns  at  Charleston  ;  Hooping  old  United  States  Cast-Iron 
Guns;  Endurance  and  Accuracy  of  the  Armstrong  600-pounder;  Competitive 
Trials  with  7-inch  Guns. 


34          SCIENTIFIC  BOOKS  PUBLISHED  BY 

•Peirce's  Analytic  Mechanics. 

4to.    Cloth.    $10.00. 

SYSTEM  OF  ANALYTIC  MECHANICS.  Physical  and  Celestial 
Mechanics.  By  BENJAMIN  PEIRCK,  Perkins  Professor  of  Astronomy 
and  Mathematics  in  Harvard  University,  and  Consulting  As 
tronomer  of  the  American  Ephemeris  and  Nautical  Almanac. 
Developed  in  four  systems  of  Analytic  Mechanics,  Celestial 
Mechanics,  Potential  Physics,  and  Analytic  Morphology. 

*'  I  have  re-examined  the  memoirs  of  the  great  geometers,  and  have  striven 
to  consolidate  their  latest  researches  and  their  most  exalted  forms  of  thought 
into  a  consistent  and  uniform  treatise.  If  I  have  hereby  succeeded  in  Open 
ing  to  the  students  of  my  country  a  readier  access  to  these  choice  jewels  of 
intellect ;  if  their  brilliancy  is  not  impaired  in  this  attempt  to  reset  them  ;  if, 
in  their  own  constellation,  they  illustrate  each  other,  and  concentrate 
a  stronger  light  upon  the  names  of  their  discoverers  ,  and,  still  more,  if  any 
gem  which  I  may  have  presumed  to  add  is  not  wholly  lustreless  in  the  collec- 
t\on,  I  shall  feel  that  my  work  has  not  been  in  vain."—  Extract  from  the  Pr& 
face. 

Bnrt's  Key  to  Solar  Compass. 

Second  Edition. 

Pocket  Book  Form.     Tuck.     $2.50.  <«-; 

KEY  TO  THE  SOLAR  COMPASS,  and  Surveyor's  Companion  ; 
comprising  all  the  Holes  necessary  for  use  in  the  field;  also, 
Description  of  the  Linear  Surveys  and  Public  Land  System  of 
the  United  States,  Notes  on  the  Barometer,  Suggestions  for  an 
outfit  for  a  Survey  of  four  months,  etc.,  etc.,  etc.  By  W.  A. 
BUST,  U.  S.  Deputy  Surveyor.  Second  edition. 


Chauvenet's  Lunar  Distances. 

8vo.    Cloth.    $2.00. 

NEW  METHOD  OF  COERECTING  LUNAR  DISTANCES, 
and  Improved  Method  of  Finding  the  Error  and  Rate  of  a  Chro 
nometer,  by  equal  altitudes.  By  WM.  CHAUVENET,  LL.D.,  Chan 
cellor  of  Washington  University  of  St.  Louis. 


Jefiers'  Nautical  Surveying. 

Illustrated  with  9  Copperplates  and  31  Wood-cut  Illustrations.     8vo» 
Cloth.      $5,00. 

NAUTICAL  SURVEYING.  By  WII.LIA*  N.  JBFFEHS,  Captain 
U.  &  Navy. 

Many  books  have  been  written  on  each  of  the  subjects  treated  of  in  the 
sixteen  chapters  of  this  work;  and,  to  obtain  a  complete  knowledge  of 
geodetic  surveying  requires  a  profound  study  of  the  whole  range  of  mathe 
matical  and  physical  sciences ;  but  a  year  of  preparation  should  render  any 
intelligent  officer  competent  to  conduct  a  nautical  survey. 

CONTENTS. — Chapter  I.  Formula?  and  Constants  Useful  in  Surveying 
II.  Distinctive  Character  of  Surveys.  III.  Hydrographic  Surveying  under 
Sail ;  or,  Running  Survey.  IV.  Hydrographic  Surveying  of  Boats ;  or,  Har 
bor  Survey.  V.  Tides— Definition  of  Tidal  Phenomenar-Tidal  Observations. 
VI.  Measurement  of  Bases — Appropriate  and  Direct.  VII.  Measurement  of 
the  Angles  of  Triangles— Azimuths— Astronomical  Bearing-s.  VIII.  Correc 
tions  to  be  Applied  to  the  Observed  Angles.  IX.  Levelling — Difference  of 
Level.  X.  Computation  of  the  Sides  of  the  Triangulation — The  Three-point 
Problem.  XI.  Determination  of  the  Geodetic  Latitudes,  Longitudes,  and 
Azimuths,  of  Points  of  a  Triangulation.  XII.  Summary  of  Subjects  treated 
of  in  preceding  Chapters — Examples  of  Computation  by  various  Formulae. 
XII 1.  Projection  of  Charts  and  Plans.  XIV.  Astronomical  Determination  of 
Latitude  and  Longitude.  XV.  Magnetic  Observations.  XVI.  Deep  Sea 
Soundings.  XVII.  Tables  for  Ascertaining  Distances  at  Sea,  and  a  full 
Index. 

List  of  Plates. 

Plate  I.  Diagram  Illustrative  of  the  Triangulation.  II.  Specimen  Page 
of  Field  Book.  III.  Running  Survey  of  i  Coast.  IV.  Example  of  a  Running 
Survey  from  Belcher.  V.  Flying  Survey  of  an  Island.  VI.  Survey  of  a 
Shoal.  VII.  Boat  Survey  of  a  River.  VIII.  Three-Point  Problem.  IX. 
Triangulation. 

Coffin's  Navigation. 

Fifth  Edition. 

12mo.     Cloth.     $3.50. 

NAVIGATION  AND  NAUTICAL  ASTRONOMY.  Prepared 
for  the  Use  of  the  U.  S.  Naval  Academy.  By  J.  H.  C.  COFFIN, 
Prof,  of  Astronomy,  Navigation  and  Surveying,  with  52  wood 
cut  illustrations. 


36          SCIENTIFIC  BOOKS  PUBLISHED  BY 

Clark's  Theoretical  Navigation. 

8vo.    Cloth.    $3,00. 

THEORETICAL  NAVIGATION  AND  NAUTICAL  ASTRON 
OMY.  By  LEWIS  CLARK,  Lieut. -Commander,  U.  S.  Navy.  Il 
lustrated  with  41  Wood-cuts,  including  the  Vernier. 

Prepared  for  Use  at  the  TJ.  S.  Naval  Academy. 


The  Plane  Table. 

Illustrated.     8vo.     Cloth.     $2.00. 

ITS  USES  IN  TOPOGRAPHICAL  SURVEYING.     From  the 
Papers  of  the  U.  S.  Coast  Survey. 

This  work  gives  a  description  of  the  Plane  Table  employed  at  the  U.  S. 
Coast  Survey  Office,  and  the  manner  of  using  it. 


Pook  on  Shipbuilding. 

9 

8vo.    Cloth.     $5.00. 

METHOD  OF  COMPARING  THE  LINES  AND  DRAUGHT 
ING  VESSELS  PROPELLED  BY  SAIL  OR  STEAM,  in 
cluding  a  Chapter  on  Laying  off  on  the  Mould-Loft  Floor.  By 
SAMUEL  M.  POOK,  Naval  Constructor.  1  vol.,  8vo.  With  illus 
trations.  Cloth.  $5.00. 


Brunnow's  Spherical  Astronomy. 

8vo.     Cloth.     $6.50. 

SPHERICAL  ASTRONOMY.     By  F.  BRITNNOW,  Ph.  Dr.    Trans 
lated  by  the  Author  from  the  Second  German  edition. 


D.  VAST  NOSTRAND.  37 


• 

Van  Buren's  Formulas. 


8vo.    Cloth.    $2.00. 

INVESTIGATIONS  OF  FORMULAS,  for  the  Strength  of  the 
Iron  Parts  of  Steam  Machinery.  By  J.  D.  VAN  BTJREN,  Jr.,  C.  E. 
Illustrated. 

This  is  an  analytical  discussion  of  the  formulae  employed  by  mechanical 
engineers  in  determining  the  rupturing  or  crippling  pressure  in  the  different 
parts  of  a  machine.  The  formulae  are  founded  upon  the  principle,  that  the 
different  parts  of  a  machine  should  be  equally  strong,  and  are  developed  in 
reference  to  the  ultimate  strength  of  the  material  in  order  to  leave  the  choice 
of  a  factor  of  safety  to  the  judgment  of  the  designer.  —Sillimaris  Journal, 


Joynson  on  Machine  Gearing. 

8vo.     Cloth.     $2.00. 

THE  MECHANIC'S  AND  STUDENT'S  GUIDE  in  the  Design 
ing  and  Construction  of  General  Machine  Gearing,  as  Eccentrics, 
Screws,  Toothed  Wheels,  etc.,  and  the  Drawing  of  Rectilineal 
and  Curved  Surfaces  ;  with  Practical  Rules  and  Details.  Edited 
by  FRANCIS  HERBERT  JOYNSON.  Illustrated  with  18  folded 
plates. 

"  The  aim  of  this  work  is  to  be  a  guide  to  mechanics  in  the  designing  and 
construction  of  general  machine-gearing.  This  design  it  well  fulfils,  being 
plainly  and  sensibly  written,  and  profusely  illustrated." — Sunday  Times. 


Barnard's  Report,  Paris  Exposition, 

1867. 

Illustrated.     8vo.     Cloth.     $5.00. 

REPORT  ON  MACHINERY  AND  PROCESSES  ON  THE 
INDUSTRIAL  ARTS  AND  APPARATUS  OF  THE  EXACT 
SCIENCES.  By  F.  A.  P.  BERNARD,  LL.D.— Paris  Universal 
Exposition,  1867. 

"  We  have  in  this  volume  the  results  of  Dr.  Barnard's  study  of  the  Paris 
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since  the  Universal  Exhibition  of  18ol,  and  we  doubt  if  anything  equal  to  it 
has  appeared  this  century."  -  Journal  Applied  Chemistry. 


38  SCIENTIFIC  BOOKS  PUBLISHED  BY 

Engineering  Facts  and  Figures. 

18mo.     Cloth.     $2.50  per  Volume. 

AN  ANNUAL  REGISTER  OF  PROGRESS  IN  MECHANI 
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1863-64-65-06-67-68.  Fully  illustrated.  6  volumes 

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Beckwith's  Pottery. 

8vo.     Paper.     60  cents. 

OBSERVATIONS  ON  THE  MATERIALS  and  Manufacture  of 
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Tiles,  with  Remarks  on  the  Products .  exhibited  at  the  London 
International  Exhibition,  1871.  By  ARTHUR  BECK  WITH,  Civil 
Engineer. 

"  Everything  is  noticed  in  this  book  which  conies  tinder  the  head  of  Pot 
tery,  from  fine  porcelain  to  ordinary  brick,  and  aside  from  the  interest  which 
all  take  in  such  manufactures,  the  work  will  be  of  considerable  value  to 
followers  of  the  ceramic  art." — Evening  Mail. 


Dodd's  Dictionary  of  Manufactures,  etc. 

12mo.     Cloth.     $2.00. 

DICTIONARY  OF  MANUFACTURES,   MINING,   MACHIN 
ERY,  AND  THE  INDUSTRIAL   ARTS.     By  GEORGE  D«DD. 

This  work,  a  small  book  on  a  great  subject,  treats,  in  alphabetical  ar 
rangement,  of  those  numerous  matters  which  come  generally  within  the  range 
of  manufactures  and  the  productive  arts.  The  raw  materials — animal,  vege 
table,  and  mineral — whence  the  manufactured  products  are  derived,  are  suc 
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branches  of  national  industry  are  conducted,  in  regard  to  values  and  quantities, 
is  indicated  in  various  ways. 


D.    VAN  NOHTltAND.  39 


Stuart's  Civil  and  Military  Engineer 
ing  of  America. 

8vo.     Illustrated.      Cloth.     $5.00. 

THE  CIVIL  AND  MILITARY  ENGINEERS  OF  AMERICA. 
By  General  CHARLES  B.  STUART,  Author  of  "  Naval  Dry  Docks 
of  the  United  States,"  etc.,  etc.  Embellished  with  nine  finely 
executed  portraits  on  steel  of  eminent  engineers,  and  illustrated 
by  engravings  of  some  of  the  most  important  and  original  works 
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Containing  sketches  of  the  Life  and  Works  of  Major  Andrew  Ellicott, 
James  Geddes  (with  Portrait",  Benjamin  "Wright  (with  Portrait),  Canvass 
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les  Ellet,  Jr.  with  Portrait),  Samuel  Forrer,  William  Stuart  Watson,  John 
A.  Roebling. 


Alexander's  Dictionary  of  Weights 
and  Measures. 

8vo.     Cloth.     $3.50. 

UNIVERSAL  DICTIONARY  OF  WEIGHTS  AND  MEAS 
URES,  Ancient  and  Modern,  reduced  to  the  standards  of  the 
United  States  of  America.  By  J.  II.  ALEXANDER.  New  edition. 
1vol. 

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search." — Scientific  American. 


Gouge  on  Ventilation. 

Third  Edition    Enlarged. 

8vo.     Cloth.     $2.00. 

NEW  SYSTEM  OF  VENTILATION,  which  has  been  thoroughly 
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40  SCIENTIFIC  BOOKS  PUBLISHED  BY 

Saeltzer's  Acoustics. 

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TEEATISE  ON  ACOUSTICS  in  Connection  with  Ventilation. 
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SAELTZER. 

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paid.  The  author's  theory  is,  that,  by  bestowing  proper  care  upon  the  point 
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Myer's  Manual  of  Signals. 

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Larrabee's  Secret  Letter  and 
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By  C.  S.  LARRABEE,  the  original  inventor  of  the  scheme. 


D.   VAN  NOSTRAND.  41 


Hunt's  Designs  for  Central  Park 
Gateways. 

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DESIGNS  FOE  THE  GATEWAYS  OF  THE  SOUTHERN 
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Pickert  and  Metcairs  Art  of  Graining. 

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THE  ART  OF  GRAINING.  How  Acquired  and  How  Produced, 
with  description  of  colors  and  their  application.  By  CHARLES 
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tinted  plates  of  the  various  woods  used  in  interior  finishing. 
Tinted  paper. 

The  authors  present  here  the  result  of  long  experience  in  the  practice  of 
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Portrait  Gallery  of  the  War, 

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PORTRAIT  GALLERY  OF  THE  WAR,  CIVIL,  MILITARY 
AND  NAVAL.  A  Biographical  Record.  Edited  by  FBANK 
MOORE. 


One  Law  in  Nature. 

12mo.    Cloth.    $1.50. 

ONE  LAW  IN  NATURE.  By  Capt.  H.  M.  LAZELLE,  U.  S.  A. 
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Identity  of  Matter,  and  its  Multiple  Atom  Constitution,  applied 
to  the  Physical  Affections  or  Modes  of  Energy. 


42  SCIENTIFIC  B  0  OKS  P  UBLISHED  B  T 

Ernst's    Manual  of  Military  En 
gineering. 

193  Wood  Cuts  and  3  Lithographed  Plates.    12mo.    Cloth.     $5.00. 

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ING.  Prepared  for  the  use  of  the  Cadets  of  the  U.  S.  Military 
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Corps  of  Engineers,  Instructor  in  Practical  Military  Engi 
neering,  U.  S.  Military  Academy. 


Church's    Metallurgical   Journey. 

24  Illustrations.    8vo.    Cloth.    $2.00. 

NOTES      OF    A     METALLURGICAL     JOURNEY     IN 
EUROPE.    By  JOHN  A.  CHURCH,  Engineer  of  Mines. 


Blake's   Precious   Metals. 

8vo.    Cloth.    $2.00. 

REPORT  UPON  THE  PRECIOUS  METALS :  Being  Statisti 
cal  Notices  of  the  principal  Gold  and  Silver  producing  regions 
of  the  World.  Represented  at  the  Paris  Universal  Exposi 
tion.  By  WILLIAM  P.  BLAKE,  Commissioner  from  the  State 
of  California. " 


Clevenger's  Surveying. 

Illustrated  Pocket  Form.    Morocco  Gilt.     $2.50. 

A  TREATISE  ON  THE  METHOD  OF  GOVERNMENT 
SURVEYING,  as  prescribed  by  the  United  States  Congress, 
and  Commissioner  of  the  General  Land  Office.  With  com 
plete  Mathematical,  Astronomical  and  Practical  Instructions, 
for  the  use  of  the  United  States  Surveyors  in  the  Field,  and 
Students  who  contemplate  engaging  in  the  business  of  Public 
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veyor. 

"  The  reputation  of  the  author  as  a  surveyor  guarantees  an  exhaustive 
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"  Surveyors  have  long  needed  a  text-book  of  this  description. — The  Press. 


D.   VAN  NOSTRAND.  43 


Bow  on  Bracing. 

156  Illustrations  on  Stone.     8vo.     Cloth.     $1.50. 

A  TREATISE  OX  BRACING,  with  its  application  to  Bridges 
and  other  Structures  of  Wood  or  Iron.  By  ROBERT  HENRY 
Bow,  C.  E. 


Howard's  Earthwork  Mensuration. 

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EARTHWORK  MENSURATION  ON  THE  BASIS  OF 
THE  PRISMOIDAL  FORMULAE.  Containing  simple  and 
labor-saving  method  of  obtaining  Prismoidul  Contents  direct 
ly  from  End  Areas.  Illustrated  by  Examples,  and  accom 
panied  by  Plain  Rules  for  practical  uses.  By  CONWAY  R. 
HOWARD,  Civil  Engineer,  Richmond,  Va. 


McAlpine's   Modern   Engineering. 

Second  Edition.     8vo.     Cloth.     $1.50. 

MODERN  ENGINEERING.    A  Lecture  delivered  at  the  Amer 
ican  Institute  in  New  York.     By  WILLIAM  J. 


Mowbray's  Tri-Nitro-G-lycerine. 

8vo.     Cloth.     Illustrated.     $3.00. 

TRI-NITRO-GLYCERINE,  as  applied  in  the  Hoosac  Tunnel, 
and  to  Submarine  Blasting,  Torpedoes,  Quarrying,  etc.  Being 
the  result  of  six  years'  observation  and  practice  during  the 
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sive,  Mica  Blasting  Powder,  Dynamites ;  with  an  account  of 


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the  various  Systems  of  Blasting  by  Electricity,  Priming  Com 
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Operative  Chemist,  with  thirteen  illustrations,  tables,  and 
appendix.  Third  Edition.  Re-written. 


Wanklyn's  Milk  Analysis. 

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MILK  ANALYSIS.  A  Practical  Treatise  on  the  Examination 
of  Milk,  and  its  Derivatives,  Cream,  Butter  and  Cheese.  By 
J.  ALFRED  WANKLY^,  M.  R.  C.  S. 


Toner's  Dictionary  of  Elevations. 

8vo.     Paper,  $3.00.     Cloth,  $3.75.  ' 

DICTIONARY  OF  ELEVATIONS  AND  CLIMATIC  REG- 
ISTER  OF  THE  UNITED  STATES.  Containing,  in  addi 
tion  to  Elevations,  the  Latitude,  Mean  Annual  Temperature, 
and  the  total  Annual  Rain  Fall  of  many  localities ;  with  a 
brief  Introduction  on  the  Orographic  and  Physical  Peculiari 
ties  of  North  America.  By  J.  M.  TOXEE,  M.  D. 


Adams.    Sewers  and  Drains. 

(In  Press.) 

SEWERS  AND  DRAINS    FOR    POPULOUS  DISTRICTS. 

Embracing  Rules  and  Formulas  for  the  dimensions  of  Sani 
tary  Engineers.  By  JULIUS  W.  ADAMS,  Chief  Engineer  of  the 
Board  of  City  Works,  Brooklyn.- 


D.  VAN  NOSTEAND.  45 


SILVER  MINING  REGIONS  OF  COLORADO,  with  some 
account  of  the  different  Processed  now  being  introduced  for 
working  the  Gold  Ores  of  that  Territory.  By  J.  P.  WHITNEY. 
12mo.  Paper,  25  cents. 


COLORADO :  SCHEDULE  OF  ORES  contributed  by  sundry 
persons  to  the  Paris  Universal  Exposition  of  1867,  with  some 
information  about  the  Region  and  its  Resources.  By  J.  P. 
WHITNEY,  Commissioner  from  the  Territory.  8vo.  Paper,  with 
Maps.  25  cents. 


THE  SILVER  DISTRICTS  OF  NEVADA.  With  Map.  8vo. 
Paper.  35  cents. 

ARIZONA :  ITS  RESOURCES  AND  PROSPECTS.  By  Hon. 
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Paper.  25  cents. 


MONTANA  AS  IT  IS.  Being  a  general  description  of  its  Re 
sources,  both  Mineral  and  Agricultural;  including  a  complete 
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with  a  Map  of  the  Territory,  showing  the  different  Roads  and 
the  location  of  the  different  Mining  Districts.  To  which  is 
appended  a  complete  Dictionary  of  THE  SNAKE  LANGUAGE,  and 
also  of  the  famous  Chinnook  Jargon,  with  numerous  critical  and 
explanatory  Notes.  By  GRANVILLE  STUART.  8vo.  Paper.  $2.00. 


RAILWAY  GAUGES.  A  Review  of  the  Theory  of  Narrow 
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SEYMOUR,  Geril.  Consulting  Engineer.  8vo.  Paper.  50  cents. 


REPORT  made  to  the  President  and  Executive  Board  of  the 
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8vo.  Paper.  75  cents. 


46  SCIENCE  SERIES  PUBLISHED  B  T 


Van   Nostrand's    Science    Series. 

It  is  the  intention  of  the  Publisher  of  this  Series  to  issue  them  at  inter 
vals  of  about  a  month.  They  will  be  put  up  in  a  uniform,  neat  and  attrac 
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of  the  highest  character. 

Price,  50  Cents  Each. 
1. 

CHIMNEYS  FOR  FURNACES,  FIRE-PLACES,  AND 
STEAM  BOILERS.  By  R.  ARMSTRONG,  C.  E. 

J3. 

STEAM  BOILER  EXPLOSIONS.    By  ZERAH  COLBURN. 

3. 

PRACTICAL  DESIGNING  .OF  RETAINING  WALLS 
By  ARTHUR  JACOB,  A.  B.  With  Illustrations. 

4. 

PROPORTIONS  OF  PINS  USED  IN  BRIDGES.  By 
CHARLES  E.  BENDER,  C.  E.  With  Illustrations. 

s. 

VENTILATION  OF  BUILDINGS.  By  W.  F.  BUTLER.  With 
Illustrations. 

e. 

ON  THE  DESIGNING  AND  CONSTRUCTION  OF  STOR 
AGE  RESERVOIRS.  By  ARTHUR  JACOB.  With  Illustra 
tions. 

7. 

SURCHARGED  AND  DIFFERENT  FORMS  OF  RETAIN 
ING  WALLS.  By  JAMES  S.  TATE,  C.  E. 

a. 

A  TREATISE  ON  THE  COMPOUND  ENGINE.  By  JOHN 
TURNBULL.  With  Illustrations. 

9. 

FUEL.     By  C.  WILLIAM  SIEMENS,  to  which  is  appended  the  value 
of  ARTIFICIAL  FUELS  AS   COMPARED   WITH   COAL. 
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A.  MALLET.     With  Illustrations. 

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